Penn State STAT 200 Assignment
truecolors# 1. Directions: Read the following problem. In your answer, please include the following information:
a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.
b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.
c. If the problem is a hypothesis test, indicated if it has a lowertail, uppertail, or twotail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.
Unless indicated otherwise, you DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc. Just type your answer to a., b., and c. above in the space below.
Problem: A large organization is being investigated to determine if its recruitment is sexbiased. Tables 1 and 2, respectively, show the classification of applicants for sales and for secretarial positions according to gender and result of interview. Table 3 is an aggregation of the corresponding entries of Table 1 and Table 2. Answer each of the following:
i. According to the data in tables 1 and 2, does there seem to be an association with gender and hiring status at the 5% significance level?
ii. Does the data in Table 3 indicate the same result?
Table 1 Sales Positions
Offered  Denied  Total  
Male  25  50  75 
Female  75  150  225 
Total
 100
 200
 300

Table 2 Secretarial Positions
Offered  Denied  Total  
Male
 150
 50
 200

Female
 75
 25
 100

Total
 225
 75
 300

Table 3 Secretarial and Sales Positions
Offered  Denied  Total  
Male
 175
 100
 275

Female
 150
 175
 325

Total
 325
 275
 600

# 2. Directions: Read the following problem. In your answer, please include the following information:
a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.
b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.
c. If the problem is a hypothesis test, indicated if it has a lowertail, uppertail, or twotail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.
You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.
Problem: An instructor at Arizona State University asked a random sample of 8 students to record their study times in a elementary statistics course. She then made a table for total hours studied over 2 weeks and test scores at the end of the 2 weeks. Here are the data:
Study time 10 15 12 20 8 16 14 22
Test Scores 92 75 86 76 92 80 84 81
Assuming that a linear association exists, how are the data correlated? Determine the exact linear relationship between study time and test scores and use it to estimate the predicted test score for a student who studies 12 hours.
# 3. Directions: Read the following problem. In your answer, please include the following information:
a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.
b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.
c. If the problem is a hypothesis test, indicated if it has a lowertail, uppertail, or twotail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.
You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.
Problem: A company sells a strong commercial floor cleaner and claims that the flashpoint (the lowest temperature at which the vapor of a combustible liquid can be ignited in air) exceeds 200ºF. A random sample of cleaner was obtained and the flashpoint of each was measured. The sample mean was 198.2ºF and the sample standard deviation was 10ºF. At the 1% significance level, is there sufficient evidence to support the companies claim?
# 4. Directions: Read the following problem. In your answer, please include the following information:
a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.
b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.
c. If the problem is a hypothesis test, indicated if it has a lowertail, uppertail, or twotail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.
You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.
Summary Table for Statistical Techniques
Inference  Parameter  Statistic  Type of Data  Examples  Analysis  Minitab Command  Conditions  
1  Estimating a mean  One population mean µ
 sample mean
 numerical  What is the average weight of adults? What is the average cholesterol level of adult females?
 1sample tinterval
 Stat >Basic statistics >1sample t
 data approximately normal or have a large sample size (n ≥ 30)

2  Test about a mean  One population mean µ
 sample mean
 numerical  Is the average GPA of juniors at Penn State higher than 3.0? Is the average Winter temperature in State College less than 42ْ F?  H_{o }: µ = µ_{o} H_{a }: µ ¹ µ_{o}or H_{a}: µ > µ_{o} or H_{a }: µ < µ_{o} The one sample t test:  Stat >Basic statistics >1sample t  data approximately normal or have a large sample size (n ≥ 30)

3  Estimating a proportion  One population proportion p
 sample proportion  categorical (binary)  What is the proportion of males in the world? What is the proportion of students that smoke?
 1proportion Zinterval
 Stat >Basic statistics >1sample proportion  n≥ 10 and n (1) ≥ 10 
4  Test about a proportion  One population proportion p
 sample proportion  categorical (binary)  Is the proportion of females different from 0.5? Is the proportion of students who fail Stat200 less than 0.1?  H_{o }: p = p_{o} H_{a }: p ¹ p_{o}or H_{a}: p > p_{o} or H_{a }: p < p_{o} The one proportion Ztest:
 Stat >Basic statistics >1sample proportion  n p_{o }³ 10andn (1p_{o }) ³ 10 
Inference  Parameter  Statistic  Type of Data  Examples  Analysis  Minitab Command  Conditions  
5  Estimating the difference of two means  difference in two population means µ_{1}µ_{2}
 difference in two sample means
 numerical  How different are the mean GPAs of males and females? How many fewer colds do vitamin C takers get, on average, than non vitamin C takers?
 twosample tinterval
See text, page 445, for the s.e. of the difference  Stat >Basic statistics >2sample t
 independent samples from the two populations data in each sample are about normal or large samples (n_{i} ≥ 30)

6  Test to compare two means  difference in two population means µ_{1}µ_{2}
 difference in two sample means
 numerical  Do the mean pulse rates of exercisers and nonexercisers differ? Is the mean EDS score for dropouts greater than the mean EDS score for graduates?  H_{o }: µ_{1} = µ_{2} H_{a }: µ_{1} ¹ µ_{2}or H_{a }: µ_{1} > µ_{2} or H_{a }: µ_{1} < µ_{2} The two sample t test: See text, page 445, for the s.e. of the difference  Stat >Basic statistics >2sample t  independent samples from the two populations data in each sample are about normal or large samples (n_{i} ≥ 30)

7  Estimating a mean with paired data  mean of paired difference µ_{D}
 sample mean of difference  numerical  What is the difference in pulse rates, on the average, before and after exercise?
 paired tinterval
 Stat >Basic statistics >Paired t  differences approximately normal or have a large number of pairs (n ≥ 30)

8  Test about a mean with paired data  mean of paired difference µ_{D}
 sample mean of difference  numerical  Is the difference in IQ of pairs of twins zero? Are the pulse rates of people higher after exercise?  H_{o }: µ_{D} = 0 H_{a }: µ_{D} ¹ 0or H_{a}: µ_{D} > 0 or H_{a }: µ_{D} < 0  Stat >Basic statistics >Paired t  differences approximately normal or have a large number of pairs (n ≥ 30)

Inference  Parameter  Statistic  Type of Data  Examples  Analysis  Minitab Command  Conditions  
9  Estimating the difference of two proportions  difference in two population proportions p_{1}p_{2}
 difference in two sample proportions
 categorical (binary)  How different are the percentages of male and female smokers? How different are the percentages of upper and lower class binge drinkers?
 twoproportions Zinterval
See notes for s.e. formula  Stat >Basic statistics >2 proportions  independent samples from the two populations n≥ 10 and (1n)≥ 10 for each sample 
10  Test to compare two proportions  difference in two population proportions p_{1}p_{2}
 difference in two sample proportions
 categorical (binary)  Is the percentage of males with lung cancer higher than the percentage of females with lung cancer? Are the percentages of upper and lower class binge drinkers different?  H_{o }: p_{1} = p_{2} H_{a }: p_{1} ¹ p_{2}or H_{a }: p_{1} > p_{2} or H_{a }: p_{1} < p_{2} The two proportion z test:
See notes for s.e. formula  Stat >Basic statistics >2 proportions  independent samples from the two populations n≥ 10 and (1n)≥ 10 for each sample 
11 
Relationship in a 2way table
 relationship between two categorical variables or difference in two or more population proportions
 the observed counts in a twoway table  categorical  Is there a relationship between smoking and lung cancer? Do the proportions of students in each class who smoke differ?
 H_{o }: The two variables are not related H_{a }: The two variables are related The chisquare statistic:  Stat >Tables >CrossTabu lation >Chi Square analysis for For summarized Data: Stat> Tables> Chi Square. 
all expected counts should be greater than 1 at least 80% of the cells should have an expected count greater than 5

Inference  Parameter  Statistic  Type of Data  Examples  Analysis  Minitab Command  Conditions  
12  Test about a slope  slope of the population regression line b_{1}
 sample estimate of the slope b_{1}  numerical  Is there a linear relationship between height and weight of a person?  H_{o }: b_{1 }= 0 H_{a }: b_{1} ¹ 0or H_{a }: b_{1} > 0 or H_{a }: b_{1} < 0 The t test with n2 degrees of freedom:  Stat >Regression >Regression  the form of the equation that links the two variables must be correct the error terms are normally distributed the errors terms have equal variances the error terms are independent of each other 
13  Test to compare several means
 Population means of the k populations µ_{1,}µ_{2,….., ,}µ_{k}
 Sample means of the k populations x_{1,}x_{2,….., ,}x_{k}  numerical  Is there a difference between the mean GPA of Freshman, Sophomore, Junior and Senior classes? 
H_{o }: µ_{1=}µ_{2=}_{˙˙˙}_{ =}µ_{k} H_{a }: not all the means are equal The F test for oneway ANOVA:
 Stat >ANOVA >Oneway  each population is normally distributed independent samples from the k populations equal population standard deviations

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