Stat Help need MCQ
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assignment3.docxPart I: z Scores and the Unit Normal Table
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1
You can only use z scores to determine the probability of a score if
A
the z score is positive
B
the z score is negative
C
the population distribution is normally shaped
D
the population distribution is negatively skewed
E
the population distribution is positively skewed
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2
If the shaded area in your sketch is larger than half of the curve, use the _____of the unit normal table.
A
body column
B
tail column
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3
What proportion of z scores are equal to or greater than a z score of +1.2 on a normal curve?
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Numeric Answer:
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4
What proportion of z scores are equal to or greater than a z score of −0.75 on a normal curve?
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Numeric Answer:
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5
What proportion of scores are equal to or less than a z score of +0.66 on a normal curve?
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Numeric Answer:
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6
What proportion of scores are equal to or less than a z score of −1.65 on a normal curve?
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Numeric Answer:
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Part II: Computing z Scores and Finding Probabilities
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7
Use a z score to determine the proportion of people in the adult population who scored better than Henry on this memory test. Assume that the population of memory scores on this test is normally distributed.
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Numeric Answer:
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8
Use a z score to determine the proportion of people in the adult population who scored better than Henry on this object naming test. Assume that the population of object naming scores on this test is normally distributed.
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9
Use a z score to determine the proportion of people in the adult population who scored better than Henry on this test. Assume that the population of Stroop test times is normally distributed.
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10
Now, Dr. Gatz needs your help to interpret the three z scores that you computed. Based on Henry’s z scores of the memory test, the object naming test, and the Stroop test, do you think Dr. Gatz should focus his future investigations on Henry’s memory systems, naming systems, or attentional systems (i.e., those assessed by the Stroop test)? Be sure you could explain your reasoning.
Multiple answers:You can select more than one option
A
memory systems
B
naming systems
C
attentional systems
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Part III: Body Temperature
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11
Did you locate the four body temperatures on the normal curve?
A
Yes
B
No
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12
Rank the four body temperatures in order from most likely to least likely
Drag and drop to order
1
A
97.5
2
B
96.9
3
C
96.5
4
D
98.0
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13
How can you use the frequency distribution histogram of the population's body temperatures to determine which of the preceding temperatures are most rare? Select all that apply.
Multiple answers:You can select more than one option
A
Scores that are the farthest from the mean are the most rare.
B
Negative z scores are more rare than positive z scores.
C
The height of the curve above a given score reflects how rare that score is; the lower the curve line the rarer the scores are at that location.
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Distribution of Sample Means and Sampling Error
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1
What is this difference between sample statistics and population parameters called?
A
Standard deviation of the score
B
Sampling error
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2
If you obtained a random sample of 25 women from this population, what is your best guess as to what the mean height will be for that sample?
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3
In general, the _____ the sample, the closer the sample statistic should be to the population parameter.
A
larger
B
smaller
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5
Which of the following is the best description of a distribution of sample means?
A
All possible sample means taken from a population
B
The set of means for all possible random samples of a given size (N) taken from a population
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6
According to the central limit theorem, the mean of the distribution of sample means will be equal to what value?
A
0
B
µ
C
σ
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7
According to the central limit theorem, the standard deviation of the distribution of sample means will be determined by what formula?
A
N σ
B
SSN−1 SSN−1
C
NΣX
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8
According to the central limit theorem, the distribution of sample means
A
is very often normally distributed.
B
will always have the same shape as the original population of scores.
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Describing Sampling Error
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1
Fill in the Blanks
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In words, sampling error is the difference between a population parameter and a
.
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2
In words, what is the standard error of the mean? Select all that apply.
Multiple answers:You can select more than one option
A
The standard deviation of the scores in a population
B
The typical distance between scores and a population mean
C
The standard deviation of the distribution of sample means
D
The typical distance between sample means of a given size from a population mean
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3
What is the relationship between sampling error and the standard error of the mean?
A
You compute the standard error when you have a population and the sampling error when you have a sample.
B
The standard error of the mean is a measure of sampling error.
C
You divide the standard error of the mean by N to get a measure of sampling error.
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Computing Sampling Error
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4
Compute the SEM.
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5
Compute the SEM.
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Numeric Answer:
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6
Compute the SEM
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Numeric Answer:
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8
Based on your calculations for questions 4 - 6, which sample size produces the most sampling error?
A
N = 9
B
N = 36
C
N = 100
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9
What is the probability of obtaining a z for a sample mean between -1 and +1?
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10a
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What the sample size is 9, 68.26% of all possible sample means are between the body temperatures of
and
.
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10b
Fill in the Blanks
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What the sample size is 36, 68.26% of all possible sample means are between the body temperatures of
and
.
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10c
Fill in the Blanks
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What the sample size is 100, 68.26% of all possible sample means are between the body temperatures of
and
.
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11
As sample size increases, the sample mean you are likely to get will be closer to the population mean (μ).
A
True
B
False
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Determining the probability of a given sample
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12
What is the probability of obtaining a sample mean of 44 or lower?
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13
Is a sample mean of 44 that is based on 27 toddlers likely or unlikely to have come from the target population of full-term toddlers with µ = 45, σ = 6?
A
Likely
B
Unlikely
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14a
What is the probability of obtaining a sample mean of 205 or lower?
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14b
Think about whether this sample mean that is based on 100 adult men likely or unlikely to have come from a target population with µ = 208, σ = 15.
A
Likely
B
Unlikely
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15a
What is the probability of obtaining a sample mean of 1,004.5 or higher?
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15b
Think about whether this sample mean that is based on 105 students likely or unlikely to have come from a target population with µ = 1,003, σ = 25?
A
Likely
B
Unlikely
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Picking the correct statistic
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17
Choose the correct statistic
A
z for an individual score
B
z for a sample mean
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18
Choose the correct statistic.
A
z for an individual score
B
z for a sample mean
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19
Choose the correct statistic.
A
z for an individual score
B
z for a sample mean
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20
Choose the correct statistic.
A
z for an individual score
B
z for a sample mean
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21
Choose the correct statistic.
A
z for an individual score
B
z for a sample mean
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An Example of Hypothesis Testing (Significance Testing)
Step 1: Examine the statistical assumptions
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1
Your study meets all four of the necessary assumptions. Match each of the statistical assumptions listed below to the fact that suggests that assumption was met.
Premise
ResponseDrag and drop to match
1
Independence
A
All students in the study took the science test under controlled conditions so each student’s score reflects his or her own knowledge of science.
2
Appropriate measurement of the IV and the DV
B
The population of science tests scores has a normal shape
3
Normality
C
The IV in this study is a grouping variable that identifies how the sample is distinct from the population and the DV is measured on an interval/ratio scale of measurement.
4
Homogeneity of variance
D
The standard deviation of the sample was SD = 21 and the standard deviation of the population was σ = 20
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Step 2: State the null and research hypotheses
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2a
Select the correct symbolic notation for the null hypothesis.
A
µtutoring>50µtutoring>50
B
µtutoring<50µtutoring<50
C
µtutoring≥50µtutoring≥50
D
µtutoring≤50µtutoring≤50
E
µtutoring>61µtutoring>61
F
µtutoring<61µtutoring<61
G
µtutoring≥61µtutoring≥61
H
µtutoring≤61µtutoring≤61
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2b
Select the correct symbolic notation for the research hypothesis.
A
µtutoring>50µtutoring>50
B
µtutoring<50µtutoring<50
C
µtutoring≥50µtutoring≥50
D
µtutoring≤50µtutoring≤50
E
µtutoring>61µtutoring>61
F
µtutoring<61µtutoring<61
G
µtutoring≥61µtutoring≥61
H
µtutoring≤61µtutoring≤61
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3a
Select the correct verbal description of the null hypothesis.
A
The population of students who receive tutoring will have a mean science test score that is equal to 50.
B
The population of students who receive tutoring will have a mean science test score that is greater than 50
C
The population of students who receive tutoring will not have a mean science test score that is greater than 50.
D
The population of students who receive tutoring will have a mean science test score that is less than 50.
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3b
Select the correct verbal description of the research hypothesis.
A
The population of students who receive tutoring will have a mean science test score that is equal to 50.
B
The population of students who receive tutoring will have a mean science test score that is greater than 50.
C
The population of students who receive tutoring will not have a mean science test score that is greater than 50.
D
The population of students who receive tutoring will have a mean science test score that is less than 50.
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Step 3: Locate the critical region
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4
You chose to use a decision criterion of α = .05. Consequently, the critical value for your hypothesis test is
A
1.96
B
1.65
C
.05
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5
I completed this in my textbook or on spare paper.
A
Yes
B
No
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Step 4: Compute the test statistic
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6
Find the deviation between the sample mean and the population mean. (M−μ)=(M−μ)=
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Numeric Answer:
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7
Compute the deviation expected due to sampling error. SEM=N σ =
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Numeric Answer:
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8
Compute the z for the sample mean. z=SEMM−μ
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Numeric Answer:
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9
What is the probability of obtaining a z score equal to or greater than the z score you computed in Question 8 (i.e., the p value)?
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Numeric Answer:
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10
Should you reject or fail to reject the null hypothesis?
A
Reject. The z is in the critical region and the p is less than .05.
B
Fail to reject. The z is not in the critical region and the p is greater than .05.
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11
Based on the statistical results, what should you say about the effect of tutoring on science test scores?
A
The results suggest that tutoring probably improved science scores.
B
The results suggest that tutoring probably did not improve science scores.
C
The results prove that tutoring improved science scores.
D
The results prove that tutoring did not improve science scores.
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Step 5: Compute the effect size and describe it
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12
Compute d to determine how many standard deviations the scores improved by and describe how effective the tutoring treatment was.
d=σM−μ
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13
How effective was your tutoring program? Based on Cohen’s recommendations, was this improvement small, medium, or large?
A
small
B
medium
C
large
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Step 6: Summarize the results
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14
Fill in the Blanks
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Fill in the blanks of the following APA style reporting statement:
The results suggest that the tutoring program improved science test scores. The sample that received the tutoring program had a significantly higher mean test score (M =
, SD =
) than in the untutored population’s test score (µ =
, σ =
), z (N =
) =
, p =
, d =
.
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Understanding the Null and Research Hypotheses
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15
Choose from the options provided below:
A
Descriptive statistics
B
Inferential statistics
C
Sample statistics
D
Population statistics
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16
Which of the following is created when a sample does not represent the population perfectly?
A
Statistical error
B
Parameter error
C
Inferential error
D
Sampling error
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17
Fill in the Blanks
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Precise expected value for sample mean if null is true =
.
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18 & 19
For questions 18 & 19, answer this combined, modified question (hint: answering questions 18 & 19 as written in the textbook can help you answer this question):
What is the value of the difference that you would expect to observe just by chance (i.e., even if tutoring did not have an effect)?
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20
Which of the following describes how you should interpret the sampling error value you computed above?
A
When the sample size is N = 16, the typical distance between possible sample means and the population mean is 5 points.
B
All possible means will be within 5 points above the population mean and 5 points below the population mean.
C
Every time a sample of 16 people is taken, it will be exactly 5 points away from the population mean.
D
A sampling error of 5 is large.
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21a
Based on the above information, what is the shape of the distribution of sample means assuming the null hypothesis is true?
A
positively skewed
B
negatively skewed
C
normal
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21b
Based on the above information, what is the mean of the distribution of sample means assuming the null hypothesis is true?
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Numeric Answer:
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21c
Based on the above information, what is the standard deviation (i.e., the standard error of the mean) of the distribution of sample means assuming the null hypothesis is true?
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Define the Critical Region
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24
Which of the following statements is most accurate?
A
The cut line’s location is determined by the sample size.
B
The cut line’s location is determined by the standard deviation of the population.
C
The cut line’s location is determined by the population mean.
D
The cut line’s location is determined by the alpha value.
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25
The z score located exactly on the cut line is called the
A
absolute value
B
critical value
C
significant value
D
immaculate value
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26
z Scores in the critical region are
A
unlikely if the null hypothesis is true.
B
likely if the null hypothesis is true
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27
Researchers reject the null hypothesis if the computed z score is
A
outside of the critical region.
B
inside the critical region.
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28
If a z score is in the critical region with an alpha of .05, the p value for that z score must be
A
less than .05
B
greater than .05
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Why Must We Assume the Null Hypothesis Is True? Why Do We Need a Null Hypothesis?
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29
Fill in the Blanks
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The null hypothesis tells us that we should expect the sample mean to be =
.
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30
In this case, if we assume that the one-tailed research hypothesis is true (i.e., that tutoring increases science test scores), we should expect the sample mean to be (choose one)
A
a specific value
B
a value in a general range
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31
Given your answer to the previous two questions, why is it necessary to test the null hypothesis rather than the research hypothesis?
A
The null hypothesis provides a specific value to compare the sample mean to, whereas the research hypothesis does not provide a specific value to compare the sample mean to.
B
The research hypothesis provides a specific value to compare the sample mean to, whereas the null hypothesis does not provide a specific value to compare the sample mean to.
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Type I Errors, Type II Errors, and Statistical Power
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32
Fill in the Blanks
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Specific value for the center of the research hypothesis distribution of sample means =
.
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33
How would the research hypothesis distribution of sample means for this second study differ from that of the first study?
A
It would be more spread out than when the sample mean was 61.
B
It would be centered on 58 rather than 61 and more spread out.
C
It would be centered on 58 rather than 61, but its spread would be the same.
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35
Even though the center of the research hypothesis distribution of sample means is based on an estimate, if the sample’s size was sufficiently large, it can be thought of as a close estimate. Which of the following explains why a larger sample size would improve one’s confidence in the estimate?
A
A larger sample size increases the standard error of the mean.
B
A larger sample size reduces the amount of sampling error we expect a sample mean to have.
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36
Why does sampling error decrease as the sample size increases?
A
Sampling error is computed by dividing the SS for the population by N. If you increase N, you decrease sampling error.
B
Sampling error is computed by dividing the population standard deviation by the square root of N. If you increase N, you decrease sampling error.
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39
First, read information on page 175 in order to help you answer this question. Then, use this image (shown on page 176) to match the areas in the image to the associated statistical outcome.
Premise
ResponseDrag and drop to match
1
Type I error (rejecting a true null)
A
Area B
2
Type II error (failing to reject a false null)
B
Area D
3
Statistical power (rejecting a false null)
C
Area C
4
Failing to reject a true null:
D
Area A
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Effect Size
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42
Fill in the Blanks
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Refer to your answers for Questions 12 & 13 to answer this question.
The mean test score for the tutoring group was
standard deviations above the mean for the population that did not receive tutoring.
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43
How would you determine how effective the tutoring was?
A
Look at the p value; the lower the p value, the more effective the treatment.
B
Look at the effect size; the greater the d, the more effective the treatment.
C
Look at the standard error of the mean; the smaller the SEM, the more effective the treatment.
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1
This study meets all of the necessary assumptions. Match each of the statistical assumptions with the fact that suggests that assumption is met.
Premise
ResponseDrag and drop to match
1
Independence
A
The interviews in which the students’ study skills were measured were conducted one student at a time under controlled conditions.
2
Appropriate measurement of the IV and the DV
B
The standard deviations of the sample and the population are similar.
3
Normality
C
The IV in this study was a grouping variable that identifies how the sample is different from the population and the DV is measured on an interval/ratio scale of measurement.
4
Homogeneity of variance
D
The sample size used in the study is greater than 30.
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2a
Select the correct one-tailed null hypothesis.
A
The population of seniors who complete the program will have interpersonal skill scores higher than 16 (µprogram > 16).
B
The population of seniors who complete the program will not have interpersonal skill scores higher than 16 (µprogram ≤ 16).
C
The population of seniors who complete the program will have interpersonal skill scores higher than 19.2 (µprogram > 19.2).
D
The population of seniors who complete the program will not have interpersonal skill scores higher than 19.2 (µprogram ≤ 19.2).
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2b
Select the correct one-tailed research hypothesis.
A
The population of seniors who complete the program will have interpersonal skill scores higher than 16 (µprogram > 16).
B
The population of seniors who complete the program will not have interpersonal skill scores higher than 16 (µprogram ≤ 16).
C
The population of seniors who complete the program will have interpersonal skill scores higher than 19.2 (µprogram > 19.2).
D
The population of seniors who complete the program will not have interpersonal skill scores higher than 19.2 (µprogram ≤ 19.2).
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3
Dr. Nice took a sample of 36 seniors from a population with a mean of µ = 16 and a standard deviation of σ = 9. The central limit theorem (CLT) allows you to describe the distribution of sample means if the null hypothesis is true. According to the CLT, what is the mean of the distribution of sample means if the null hypothesis is true?
A
16
B
30
C
5
D
1.5
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4
According to the CLT, what is the standard deviation of the distribution of sample means (i.e., SEM) if the null hypothesis is true?
A
16
B
30
C
5
D
1.5
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5
According to the CLT, what is the shape of the distribution of sample means if the null hypothesis is true?
A
Normally distributed
B
The same as the original population of scores
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6
What is the critical value for this one-tailed test with an alpha of .05?
A
1.65
B
1.96
C
18.2
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7
If the alpha value is .05. What is the probability that the researchers will make a Type I error if the null hypothesis is true?
A
0
B
.01
C
.05
D
.95
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8
Which of the z scores on the distribution could occur if the null hypothesis is true?
A
Any z score could occur if the null hypothesis is true.
B
Only the z scores in the critical region could occur if the null hypothesis is true.
C
Only the z scores outside of the critical region could occur if the null hypothesis is true.
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9
The z scores in the critical region are values that are
A
likely to occur if the null hypothesis is true.
B
unlikely to occur if the null hypothesis is true.
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10
What do you do if the computed z score (i.e., the obtained z score) is in the critical region?
A
Reject the null hypothesis because that outcome could not occur if the null hypothesis is true
B
Reject the null hypothesis because that outcome is unlikely to occur if the null hypothesis is true
C
Fail to reject the null hypothesis because that outcome could not occur if the null hypothesis is true
D
Fail to reject the null hypothesis because that outcome is unlikely to occur if the null hypothesis is true
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11
Compute the obtained z score for this study.
A
1.5
B
1.65
C
2.13
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12
Should Dr. Nice reject or fail to reject the null hypothesis?
A
Reject the null hypothesis
B
Fail to reject the null hypothesis
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13
Which of the following is the best interpretation of the results of this study?
A
The program definitely improved the interpersonal skills of seniors.
B
It is likely that the program improved the interpersonal skills of seniors.
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14
Dr. Nice obtained a z score of 2.13 for the sample of 36 seniors. What is the probability of obtaining a z score of 2.13 or higher if the null hypothesis is true? (Determine if you need the body or tail probability from the unit normal table to answer this question.)
A
.9834
B
.0166
C
.7645
D
.0343
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15
Which of the following is a rule that indicates how you can use the p value (i.e., your answer to the previous question) to determine if you should reject the null hypothesis?
A
Reject the null if p > 1.65
B
Reject the null if p < 1.65
C
Reject the null if p < .05
D
Reject the null if p > .05
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16
In the null distribution, values that are farther from the population mean (or a z score of 0) are ______ likely than values that are closer to the population mean.
A
less
B
more
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17
The p value is the probability of getting the obtained z score or one more extreme if the null hypothesis is true. (Hint: Remember that the distribution of sample means represents all possible outcomes if the null hypothesis is true.)
A
True
B
False
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18
The p value is the probability of making a Type I error.
A
True
B
False
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19
The p value is the probability that the null hypothesis is true.
A
True
B
False
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20
You obtain a z score of 1.52. What is the p value?
A
.9357
B
.0643
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21
You obtain a z score of 1.41 with a p value of .0793. Should you reject or not reject the null hypothesis?
A
Reject
B
Fail to reject
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22
You obtain a z score that is not in the critical region; the p value must be
A
greater than alpha (.05).
B
less than alpha (.05).
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23
You obtain a z score that is in the critical region; the p value must be
A
greater than alpha (.05).
B
less than alpha (.05).
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24
You obtain a z score with a p value of .02; the z score must be
A
in the critical region.
B
outside of the critical region.
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Putting it all together
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49
How could the sample size be manipulated to maximize the likelihood that their drug would be found to be “significantly better,” even if the drug’s actual effectiveness is only slightly better than that of the competitor’s drug?
A
Using a very large sample size can result in rejecting the null hypothesis even if the drug is only slightly better than the competitor’s drug.
B
Using a very large sample size can result in obtaining a very large effect size even if the drug is only slightly better than the competitor’s drug.
C
Using a very large sample size can result in failing to rejecting the null hypothesis even if the drug is much better than the competitor’s drug.
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50
How could you convince doctors that the difference between the effectiveness of the Old Drug and that of the New Drug is not really important, even though it was statistically significant in the studies conducted by the above pharmaceutical company?
A
Compute the z scores and show them that the z is much larger for the New Drug than the Old Drug.
B
Compute the exact p value and explain that this very small p value shows that the difference between the two drugs is actually very small
C
Compute the effect size and explain that the actual difference between the drugs is very small.
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51
Is this a legitimate option in this case?
A
Yes, the researchers are justifiably concerned about making a Type II error and using an alpha of .10 reduces the probability of making this type of error.
B
Yes, the researchers are justifiably concerned about making a Type I error and using an alpha of .10 reduces the probability of making this type of error.
C
No, the researchers are justifiably concerned about making a Type II error and using an alpha of .10 increases the probability of making this type of error.
D
No, the researchers are justifiably concerned about making a Type I error and using an alpha of .10 increases the probability of making this type of error.
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52
Is this a legitimate option in this case?
A
In this case, the researchers are investigating a treatment for a relatively minor problem and treatments already exist. Using an alpha of .10 is a good idea because it will help maximize the statistical power and minimize the probability of making a Type II error.
B
Using an alpha of .10 is not acceptable because it would increase the Type I error rate. Although Type II errors would go down, there is little reason to be overly concerned with Type II errors in this study. Because current treatments exist for coughs, incorrectly failing to reject the null should not be the primary concern.
C
It does not matter if the researcher uses an alpha of .10 or .05. Either is acceptable as long as they use a very large sample size.
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53
Based on these data, which two researchers would you recommend receive the research grant? Be sure you could explain your answer using effect sizes, sample sizes, and the results of the hypothesis test.
Multiple answers:You can select more than one option
A
Study 1
B
Study 2
C
Study 3
D
Study 4
E
Study 5
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