A Catholic priest believes that a higher proportion of women in his congregation regularly

attend services than the men in his congregation. He randomly selects 100 men and 100
women from his congregation and finds that 32 men and 48 women regularly attend.

a. Specify the competing hypotheses to test the priest's claim.

b. Calculate the value of the relevant test statistic.

c. Compute the p-value. Does the evidence support the priest's claim at the 1% significance
level?

A candidate in a local election thinks seniors are by far her best supporters. She believes that
the difference in the support between seniors and nonseniors is more than 15%. To verify this
belief, the team samples 100 seniors and 150 non-seniors to find what proportion of each
group supports the candidate. It is found that 50 of the seniors support her and 36 of the non-
seniors support her.

a. Specify the hypotheses to determine if the difference in the support between seniors and
non-seniors is more than 15%.

b. Calculate the value of the test statistic and the p-value.

c. Make a conclusion at the 5% significance level.

The sales price (in $1,000) of three-bedroom apartments in two cities—Houston, Texas, and
Orlando, Florida—are given in the following table. Houston is known to have lower house prices
than Orlando; however, it is not clear if it also has lesser variability in its prices.

Houston 189 145 220 205 225 275 248 310 150 318
Orlando 301 279 224 400 249 205 289 350 218 300

a. State the null and the alternative hypotheses to determine if the variance of house price in
Houston is less than that in Orlando.
b. What assumption regarding the population is necessary to implement this step? 
c. Test the hypothesis at α = 0.05. What is your conclusion?

Two students, Mary and Joanna, are in a statistics class working hard on the consistency of their
performance in the weekly class tests. In particular, they are hoping to bring down the variance of
their test scores. Their professor believes that the students are not equally consistent in their tests.
Over a 12-week period, the test scores of these two students are shown below. Assume that the two
samples are drawn independently from normally distributed populations.

Mary 32 48 46 30 47 32 33 32 46 28 35 37
Joanna 39 44 37 45 42 44 32 33 31 35 41 40

a. Develop the hypotheses to test whether the two students differ in consistency. 
b. Use the critical value approach to test the professor's claim at α = 0.05.

A fund manager suspects there is an interaction between fund market cap (either small, mid, or
large) and the fund objective (either growth or value) on the average annual fund performance. The
fund manager obtains data and produces the following incomplete two-way ANOVA table.

Source of Variation SS df MS F
Market Cap 345.1      
Objective        18.39
Interaction        
Error   18  14.26  
Total 1,167.4      

a. Complete the ANOVA table. 

b. At the 5% significance level, can you conclude there is interaction between market cap and
objective? 

c. Are you able to conduct tests on the main effects? If yes, conduct these tests at the 5%
significance level.

A career counselor wants to understand if the average salary differs by educational attainment
blocking on industry. The counselor uses four degree levels (high school, undergraduate, master's,
and doctoral) and three industries. The study resulted in the following incomplete ANOVA table.

Source of Variation SS df MS F
Industry 7.17      
Education     46.11  
Error 9.5 6    
Total        

a. Complete the ANOVA table. 

b. At the 5% significance level, can you conclude the average salary differs by educational
attainment? 

c. At the 5% significance level, can you conclude the average salary differs by industry?

A researcher analyzes the factors that may influence the poverty rate and estimates the
following model: y = β0 + β1x1 + β2x2 + β3x3 + ε, where y is the poverty rate (y, in %), x1 is
the percent of the population with at least a high school education, x2 is the median income
(in $1,000s), and x3 is the mortality rate (per 1,000 residents). The researcher would like to
construct interval estimates for y when x1, x2, and x3 equal 85%, $50,000, and 10,
respectively. The researcher estimates a modified model where poverty rate is the response

variable and the explanatory variables are now defined as = x1 - 85, = x2 - 50, and

= x3 - 10. A portion of the regression results is shown in the accompanying table.

Regression Statistics
R Square 0.86
Standard Error 1.30
Observations 39

Standard Lower Upper

 
Coefficients Error t-stat p-value 95% 95%
Intercept 14.89 0.37 39.73 1.04E-30 14.14 15.64
−0.44 0.06 −6.81 6.68E-08 −0.57 −0.31

-0.18 0.03 -6.14 4.97E-07 -0.24 -0.12

0.17 0.19 0.87 0.3898 -0.22 0.56

a. According to the modified model, what is the point estimate for the poverty rate when x1,
x2, and x3 equal 85%, $50,000, and 10, respectively.
b. According to the modified model, what is a 95% confidence interval for the expected
poverty rate when x1, x2, and x3 equal 85%, $50,000, and 10, respectively? (Note that t0.025,35
= 2.030.)
c. According to the modified model, what is a 95% prediction interval for the poverty rate
when x1, x2, and x3 equal 85%, $50,000, and 10, respectively? (Note that t0.025,35 = 2.030.)

A marketing manager examines the relationship between the attendance at amusement parks
and the price of admission. He estimates the following model: Attendance = β0 + β1 price + ε,
where Attendance is the average daily number of people who attend an amusement park in
July (in 1,000s) and Price is the price of admission. The marketing manager would like to
construct interval estimates for Attendance when Price equals $80. The researcher estimates a
modified model where Attendance is the response variable and the Price is now defined as
Price* = Price – 80. A portion of the regression results is shown in the accompanying table. 

Regression Statistics
R Square 0.62
Standard Error 21
Observations 30
 Standard Lower Upper
 
Coefficients Error t-stat p-value 95% 95%
Intercept 86.8 4.2 20.85 1.4E-18 78.2 95.4
Price* −3.1 0.5 −6.69 2.9E-07 −4.0 −2.1

a. According to the modified model, what is the point estimate for Attendance when Price
equals $80? 

b. According to the modified model, what is a 95% confidence interval for Attendance when
Price equals $80? (Note that t0.025,28 = 2.048.)

c. According to the modified model, what is a 95% prediction interval for Attendance when
Price equals $80? (Note that  t0.025,28 = 2.048.)

A university advisor wants to determine if there is a difference in the total amount of time spent
studying between students taking an online version and a traditional class version of a certain
course. The following table contains the sample sizes of each group, and the rank sums for the
Wilcoxon rank-sum test.

  Online Traditional
Sample Size 10 12
Sum of Ranks 94.5 158.5

a. Specify the competing hypothesis to determine whether the median study time for online
students differs from the median study time for traditional students.
b. What is the value of the Wilcoxon rank-sum test statistic W?
c. Assuming W follows a normal distribution, what is the value of the corresponding test
statistic?
d. At the 1% significance level, what is the decision and conclusion?