Answers to Statistical Questions

Question 1
Confounding means a difference between the treatment and control groups, other than the treatment, which affects the responses being studied.
True
False
Question 2
To find out the percentage of individuals who are Democrats, a researcher asks his family members and his friends whether they are Democrats. This will give a random sampling.
True
False
 Question 3
Observational studies can establish association and association proves causation.
True
False
 Question 4
In a study of comparing two drugs, A and B, 100 patients are selected and given drug A, another 100 patients are selected and given drug B. The patients' responses are recorded. True or False: This is a controlled experiment.
True
False
Question 5
A random sample of 1500 adults is taken. Their opinions about the performance of the President are recorded. True or False: This is a controlled experiment.
True
False

Question 6
A Spanish survey of the health records of 2000 people showed that people in the coastal areas of Sppain are more inclined to suffer from lung problems than those in the mountainous areas. Which of the following is correct?
a.This study proves that mountain people are healthier than other English ones.
b.The sample size was too small for any conclusions to be drawn.
c.This was a controlled experimental study.
d.This is an observational study and firm conclusions are difficult to draw.
e.The placebo effect explains why so many coastal people were affected by lung problems.
Question 7
Which one of the following is true about observational studies?
a.Confounding variables are never a problem--they affect only experimental studies with true random samples for the treatment and control groups.


b. Such studies always use a placebo.
c. Confounding variables or influences are hard to deal with and it is therefore often difficult to draw firm conclusions from such studies.
d. They are the same as experimental studies without a treatment group.
e.They are more reliable than controlled experimental studies of the same size since the treatment group can be much larger than the control group.
 Question 8
Confounding influences(or variables) in an observational study are:
a.Often not easy to detect by the statistician, and are basically diffferences between the control group and the treatment group other than the treatment itself.
b.Caused by accidentally assigning some members of the treatment group to the control group.
c.Confusions in the study--usually because of the incorrectly calculated or applied formulas.
d.Corruption of the data by sloppy workers.
 Question 9
The best way to eliminate confounding factors is to:
a. choose very large samples for the treatment group
b.carefully go over the data again
c.randomly choose the treatment and control group from the population.
d.pay closer attention to the treatment group than to the control group in a doluble blind study.
e. use a placebo.
Question 10
For the given table, make a histogram, then find how many subjects are in the class interval from 9-12. There are 250 total subjects.
Educational Level(in Years) Frequency Percent
For the given table, make a histogram, then find how many subjects are in the class interval from 9-12.    There are 250 total subjects.

Educational Level(in Years)    Frequency  Percent

0-5                                                   15                 6

5-8                                                    25                10

8-9                                                    35                 14

9-12                                                _____            18

12-13                                              75                    30

13-16                                               30                ______

16-17                                               25                  10

a.35
b.45
c.47
d.75
e.

Question 11
For the histogram that could be created relative to the table in #10, find the height of the block over 13-16.
a.3.33
b.8
c.0.03
d.4
Question 12
For the histogram that could be created relative to the table in #10, find the 23rd percentile.
a.12
b.8
c.8.5
d.5
Question 13
For the histogram that could be created relative to the table in #2, which of the following intervals is the most crowded?
a.9-12
b.13-16
c.8-9
d.12-13
Question 14
For the given list, find the outlier(s): 41, 41, 8, 69, 26, 29, 19, 21, 23, 34, 39, 36, 45, 35, 36.
a.there are none
b.69
c.68
d.8, 69
e.8
Question 15
Find the average for: 8, 9, 14, -5, -26, 18, -4
a.2
b.14
c.3
d.12
e.3.5
Question 16
For the given set of numbers, find the Standard deviation: 57.9, 78, 96, 0, -14, 15, 3.
a.39.88
b.24.8
c.12.8
d.33.7
e.43.07
Question 17
For the given list, find the median: 188, 98, 41, 0, 68, 143, 193, 169.
a.120.5
b.115
c.112.5

d.34
e.4.5
 Question 18
Bias is a kind of chance error.
a.False
b.True
Question 19
Bias in measurement theory is called ____________.
a.sampling error
b.chance error
c.systematic error
Question 20
For a histogram with a long left-hand tail, the median is _______________ than the mean.
a.the same as
b.less
c.greater
Bias can be measured by taking the SD of repeated measurements.
a.True
b.False

Question 21
A die will be rolled some number of times, and you win $1 if it shows a three less than 25% of the time. Which is better?
a. 70 rolls
b. 700 rolls
Question 22
Find the area under the Normal Curve from -2.5 to 1.1.
a.82.85%
b.98.76%
c.25.89%
d.72.87%
e.12.95%

Question 23
For the women age 18-24 in the HANES2 sample, the average height was about 65.2 inches, and the SD was about 1.9 inches. Estimate the percentage of women with heights above 65 inches.
a.68.27%
b.92.03%
c.7.97%
d.46.02%
e.53.99%
Question 24
If a set of numbers has an average of 15 and an SD of 3, and each number in the set is multiplied by 4, what will the SD of the new set of numbers be?

a.7
b.10
c.14
d.12
e.60
Question 25
Sixteen people in a room have an average height of 5'6". A seventeenth person enters the room. How tall would he have to be to raise the average height by one inch?
a.6"11"
b.6'2"
c.5'8"
d.6'1"
e.6'5"
Question 26
A card is picked at random from a shuffled deck. What is the probability that it is either red or a king?
a.28/52
b.30/52
c.19/52
d.17/52
e.18/52
Question 27
The heights of the men age 18 and over in the HANES sample averaged 68.5 inches; the SD was 2.9 inches. Use the normal curve to estimate the percentage of these men with heights between 65 and 68 inches.
a.none of these
b.44.46%
c.32.54%
d.76.99%
e.11.92%

Question 28
The average on an exam was 23.5 and the SD was 5.5. Use the normal curve to estimate the percentage of students who made between 18 and 29.

a.55%
b.95.43%
c.68.27%
d.16.64%
e.20%
Question 29

A box contains a circle with a 6 in it, a square with a 3 in it, a circle with a 1 in it, and a square with a 1 in it. Say whether shape and number are independent or dependent.

a.Independent
b.Cannot be determined from the given information.
c.Dependent
Question 30
A coin is tossed twice. Find the chance that you get at least 1 tail.
a.2/3
b.7/8
c.1/4
d.1/2
e.3/4
Question 31
A coin is tossed, and you win $1 if you get less than 40% heads. How many tosses should you make?
a.10
b.100

Question 33
A box has three red balls and four green balls. A gambler bets $1 on red. A ball is randomly chosen. The gambler win $1 if the ball is red, otherwise he loses $1. He will play this game 200 times. The SE for the gambler's net gain is:
a.$52.70
b.$54.13
c.$15.56
d.$42.12
e.$14.00
Question 34
A box contains two red marbles and one blue marble. A marble is randomly selected, and you win a dollar if there are more than 60% red marbles. Choose one of the following that is better.
a.10 selections
b.100 selections
Question 35
A gambler plays roulette, and makes a $1 bet on four numbers, 400 times. The bet pays 8 to 1. Find the amount of money the CASINO is expected to make.





a.$52.63
b.$210.53
c.$33.33
d.$-21.05
e.$21.05
 Question 36
A gambler plays roulette, and makes a $1 bet on four numbers, 400 times. The bet pays 8 to 1. Find the SD of the box model that would go with this situation.
a.$56.75
b.$61.76
c.none of these
d.$2.76
e.$5.37
Question 37
A gambler plays roulette 200 times, betting $1 on a split each time. A split pays 17 to 1, and there are 2 ways in 38 to win. (We are interested in the the casino making more than $10.) Find the casino's standard error for the sum.
a.none of these
b.$10.53
c.$3.10
d.$56.84
e.$4.02

Question 38
A gambler plays roulette 200 times, betting $1 on a split each time. A split pays 17 to 1, and there are 2 chances in 38 to win. Find the chance that the casino makes more than $10 from these plays.
a.3.60%
b.50.00%
c.7.5%
d.69.19%
e.24.56%

Question 39
A gambler bets $1 on the number "19" 1600 times in roulette. This bet pays 35 to 1. What is the give-or-take on the estimate of his winnings?
a.$23.50
b.$230.50


c.$84.36
d.$184.25
e.$96.58

Question 40
A gambler plays roulette, and makes a $1 bet on four numbers, 400 times. The bet pays 8 to 1. Find the chance that the casino will win between $30 and $40.
a.63.69%
b.15.45%
c.7.88%
d.7.73%
e.83.85%
Question 41

A gambler plays roulette, and makes a $1 bet on four numbers, 400 times. The bet pays 8 to 1. Find the standard error for the sum.
a.$55.24
b.$56.76
c.none of these
d.$15.80
e.$61.76
Question 42
A group of 50,000 tax forms has 20% with gross income over $50,000. A group of 900 forms is chosen at random for audit. A box model is used to work out the expected value and the standard error for the percentage of people with incomes over $50,000 in the sample. Choose what best describes "sample size".
a.900
b.180
c.Box
d.Percentage of 1s among the draws
e.20%
Question 43
A person randomly picks 5 counties out of a state. He then randomly picks 2 town from each county picked. He then randomly picks 3 households from each town. He then interviews each person in the household to see what their preference is with regard to sports: Football, Baseball, Hockey, or Basketball. What type of sampling is this?
a.Multistage Cluster Sampling


b.Quota Sampling





c.none of these
d.Convenience Sampling

e.Simple Random Sampling
Question 44
A probability histogram represents chance by area.
a.True
b.False
Question 45
A spinner has three numbers on it(1,2,3). Each number has an equal probability of being hit on each spin. A person bets $1 to play the game. He picks a number, then he spins. If his number comes up, he wins $2. He plays this game 100 times. What would be the average amount won per spin on the spinner?
a.$0.00
b.$1.00
c.-$1.00
d.$100
e.$200
Question 46
As a person increases the number of tosses of a fair coin, the actual number of heads will get further and further away from the number of tosses divided by two.
a.False
b.True
Question 47
Find the probability that three cards are drawn from a deck, and you get two reds, followed by a black.
a.1/5100
b.169/1020
c.1/11050
d.13/102
e.none of these

Question 48
We toss a die 300 times. Find the standard error for the expected number of 3s.
a.7.06
b.6.45
c.0.3727
d.3.73
e.0.022

.
Question 49
We toss a die 300 times. What is the chance that we get more than sixty 3s?
a.87.89%
b.0.35%
c.87.90%
d.12.11%
e.6.06%
Question 50
g
a.
b.
c.

d.

e.


0 points


Question 51
You have hired a polling organization to take a simple random sample from a box of 200,000 tickets and estimate the percentage of 1s in the box. Unknown to them, the box contains 50% 0s and 50% 1s. How far off should you expect them to be if they draw 50,000 tickets?
a.1.50%
b.0.17%
c.0.20%
d.0.23%
e.0.19%
1.34 points
The probability histogram for the average of the draw will follow the normal curve, even if the contents of the box do not, as long as the histogram is put into standard units, and the number of draws is large.
a.False
b.True

Question 53
The population of interest for "Dancing with the Stars" is all of the people who watched the show. From this population, people call in for their favorite. What is the best description of bias that takes place?





a.selection bias
b.simple random sampling
c.non-response bias
d.none of these
e.cluster bias
Question 54
There are 10 workers and 2 administrators in a company meeting room. Two people will be selected at random without replacement. The chance that both are administrators is:
a.1/66
b.1/36
c.2/33
d.none of these
e.1/3
1.34 points
Question 55
h
a.
b.
c.
d.
e.
0 points
Question 56
In cluster sampling, the sample is hand-picked to resemble the population.
a.True
b.False
1.34 points
Question 57
In a certain city, there are 100,000 persons age 18 to 24. A simple random sample of 500 such persons is drawn, of whom 198 turn out to be currently enrolled in college. Estimate the percentage of all persons age 18 to 24 in that city who are currently enrolled in college.
a.39.6%
b.40%
c.38.8%

d.39.2%
e.41.1%

.

1.34 points
Question 58

In a certain city, there are 100,000 persons age 18 to 24. A simple random sample of 500 such persons is drawn, of whom 198 turn out to be currently enrolled in college. If possible, find a 95% confidence interval for the percentage of all persons age 18 to 24 in that city who are currently enrolled in college.
a.36.72% to 45.48%
b.35.22% to 43.98%
c.none of these
d.not possible
e.33.06% to 40.41%

Question 59
A researcher wants to compare the English test scores of urban high school students and rural high school students. A simple random sample of 180 urban high school students is taken with a sample average of 88 and a SD of 7. An independent simple random sample of 150 rural high school students is taken with a sample average of 86 and an SD of 8. Let the population diff=pop avg for urban students - pop avg for rural students. The null hypothesis is that the population difference = 0. The alternative hypothesis is that the population difference is greater than 0. Find the sample average difference.

a.2
b.1
c.7
d.8
e.none of these
Question 60
A researcher wants to compare the English test scores of urban high school students and rural high school students. A simple random sample of 180 urban high school students is taken with a sample average of 88 and a SD of 7. An independent simple random sample of 150 rural high school students is taken with a sample average of 86 and an SD of 8. Let the population diff=pop avg for urban students - pop avg for rural students. The null hypothesis is that the population difference = 0. The alternative hypothesis is that the population difference is greater than 0. Find the value of p.

a.10%

b.5%
c.2.8%
d.0.8%
e.7.2%

.

1.34 points

Question 61
A researcher wants to compare the English test scores of urban high school students and rural high school students. A simple random sample of 180 urban high school students is taken with a sample average of 88 and a SD of 7. An independent simple random sample of 150 rural high school students is taken with a sample average of 86 and an SD of 8. Let the population diff=pop avg for urban students - pop avg for rural students. The null hypothesis is that the population difference = 0. The alternative hypothesis is that the population difference is greater than 0. True or False: The test indicates that the observed difference is due to chance.
a.True

b.False
1.34 points
Question 62
A researcher wants to compare the English test scores of urban high school students and rural high school students. A simple random sample of 180 urban high school students is taken with a sample average of 88 and a SD of 7. An independent simple random sample of 150 rural high school students is taken with a sample average of 86 and an SD of 8. Let the population diff=pop avg for urban students - pop avg for rural students. The null hypothesis is that the population difference = 0. The alternative hypothesis is that the population difference is greater than 0. The null hypothesis is:
a.accepted
b.rejected
1.34 points

Question 63
A researcher wants to compare the English test scores of urban high school students and rural high school students. A simple random sample of 180 urban high school students is taken with a sample average of 88 and a SD of 7. An independent simple random sample of 150 rural high school students is taken with a sample average of 86 and an SD of 8. Let the population diff=pop avg for urban students - pop avg for rural students. The null hypothesis is that the population difference = 0. The alternative hypothesis is that the population difference is greater than 0. Find the value of the test statistic.
a.6.22
b.2.39
c.1.90
d.3.77
e.1.50
Question 64



A researcher wants to study the spending habits of customers of a local shopping mall. The mall manager claims that the average spending per customer is $70, but the researcher believes that the average is less than $70. A simple random sample of 350 shoppers is obtained. The sample average is $65 and the sample SD is $27. Find the SE for the sample average.
a.1.27
b.1.44
c.5.08
d.2.91
e.1.34
1.34 points
Question 65

A researcher wants to study the spending habits of customers of a local shopping mall. The mall manager claims that the average spending per customer is $70, but the researcher believes that the average is less than $70. A simple random sample of 350 shoppers is obtained. The sample average is $65 and the sample SD is $27. Find the alternative hypothesis.
a.none of these
b.the population average is less than $70
c.the population average is greater than $70
d.the population average is $70
e.the sample average is less than $70
1.34 points
Question 66
A researcher wants to study the spending habits of customers of a local shopping mall. The mall manager claims that the average spending per customer is $70, but the researcher believes that the average is less than $70. A simple random sample of 350 shoppers is obtained. The sample average is $65 and the sample SD is $27. Find the null hypothesis.
a.the population average is less than $70
b.the sample average is less than $70
c.the population average is greater than $70
d.the population average is $70
e.none of these
1.34 points
Question 67
ga.1.90%
b.6.68%
c.1.79%
d.25%
e.3.57%
0 points


Question 68

h
a.
b.
c.
d.
e

Question 69
A researcher wants to study the spending habits of customers of a local shopping mall. The mall manager claims that the average spending per customer is $70, but the researcher believes that the average is less than $70. A simple random sample of 350 shoppers is obtained. The sample average is $65 and the sample SD is $27. Should we believe the mall manager's claim?
a.No
b.Yes
1.34 points
Question 70

A researcher wants to study the spending habits of customers of a local shopping mall. The mall manager claims that the average spending per customer is $70, but the researcher believes that the average is less than $70. A simple random sample of 350 shoppers is obtained. The sample average is $65 and the sample SD is $27. We should _________ the null hypothesis.

a.Reject

b.Accept
1.34 points
Question 71
There are 10 workers and 2 administrators in a company meeting room. Two people will be selected at random without replacement. The chance that the second person is a worker given that the first person is an administrator is:
a.5/6
b.5/33
c.10/11
d.none of these
e.15/66
1.34 points
Question 72





There are 5 Democrats, 6 Republicans, and 4 Independents in a room. Two people will be selected at random without replacement. The conditional probability that the second person is an Independent, given that the first person is a Republican is:

a.1/22
b.4/15
c.none of these
d.2/7
e.2/5
1.34 points
Question 73
The standard deviation is a measure of ________________.
a.spread
b.center
2 points
Question 74
The sum of the draws from a box is 440. If the average of these draws is 2.20, how many draws were there?
a.968
b.200
c.880
d.impossible to tell
e.20
1.34 points
Question 75

A _____________ is taken from the _____________ in order to estimate the ________________.
a.population, sample, statistic
b.sample, population, statistic
c.sample, population, parameter
d.population, sample, parameter