SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1) In an exit poll, 42 of 75 men sampled supported a ballot initiative to raise the local sales tax to build a new football stadium. In the same poll, 41 of 85 women sampled supported the initiative. Find and interpret the p-value for the test of hypothesis that the proportions of men and women who support the initiative are different.	1)  _____________

2) A government housing agency is comparing home ownership rates among several immigrant groups. In a sample of 235 families who emigrated to the U.S. from Eastern Europe five years ago, 165 now own homes. In a sample of 195 families who emigrated to the U.S. from Pacific islands five years ago, 125 now own homes. Write a 95% confidence interval for the difference in home ownership rates between the two groups. Based on the confidence interval, can you conclude that there is a significant difference in home ownership rates in the two groups of immigrants?  	2)  _____________

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.
3) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Suppose 45 of the females and 60 of the males responded that they were able to give blood. Find the test statistic that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood.	3) _______

A) z = 1.645	B) z = 2.01	C) z = 1.96	D) z = 1.93

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.
4) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let  be the true mean weight of individuals before starting the diet and let  be the true mean weight of individuals after 3 weeks on the diet.

Summary information is as follows  = 5,  = 1.58.

Test to determine if the diet is effective at reducing weight. Use α = .10.	4)  _____________

A random sample of 13 men and 19 women in a college class reported their grade point averages (GPAs). Here are histograms from the data

Summary statistics for these data are
		
5) A woman in the class says that she believes that college women tend to have higher GPAs than do college men. Does this sample support her claim? Test an appropriate hypothesis and state your conclusion.	5)  _____________

A total of 23 Gossett High School students were admitted to State University. Of those students, 7 were offered athletic scholarships. The school's guidance counselor looked at their composite ACT scores (shown in the table), wondering if State U. might admit people with lower scores if they also were athletes. Assuming that this group of students is representative of students throughout the state, what do you think?

6) Test an appropriate hypothesis and state your conclusion.	6)  _____________

1)  1 ≈ .56 and 2 = .48; The test statistic is z =  ≈ 1.01
The p-value is p = 2(.5 - .3438) = .3124. The probability of observing a value of z more contradictory to the null hypothesis is .3124.
2)  1 ≈ .70 and 2 = .64;  
The confidence interval is (.70 - .64) ± 1.96≈ .06 ± .089.
Since the confidence interval includes 0, we cannot conclude that there is a difference in home ownership rates.
3) D
4) To determine if the diet is effective at reducing weight, we test

       = 0
       > 0
The test statistic is t =  =  = 7.07.

The rejection region requires  in the upper tail of the t distribution with  The rejection region is t > 1.533.

Since the observed value of the test statistic falls in the rejection region (t = 7.07 > 1.533),  is rejected. There is sufficient evidence to indicate that the diet is effective at reducing weight when testing at α = .10.
5)   -  = 0,   -  > 0  where M = men and W = women
* Independent group assumption Men and women are definitely independent groups.
* Randomization condition We are told that these are random samples of men and women in the class.
* 10% condition These samples represents less than 10% of all possible men and less than 10% of all possible women taking the course.
* Nearly Normal condition The samples are pretty small, but the histograms given don't seem to deviate too badly from being unimodal and symmetric.

Because the conditions are satisfied, it is appropriate to model the sampling distribution of the
difference in the means with a Student's t-model, and we will perform a two-sample t-test.
We know 	 = 19		  = 3.330		 = 0.395
			 = 13		  = 2.898		 = 0.583
SE( - ) =  =  =  =  = 0.185
The observed difference is  -  = 3.330 - 2.898 = 0.432.
t =  =  = 2.335
The sampling distribution model has 19.44 degrees of freedom. 
P( > 2.335) = 0.0152.

This P-value is low, so we reject the null hypothesis. There is evidence that college women have a higher mean GPA than do college men.
6) Let mean ACT score of non-athletes =  and mean ACT score of athletes = 
  -  = 0 ,   -  > 0
* Independent group assumption Non-athletes and athletes are definitely independent groups.
* Randomization condition These are not random samples, but they should be representative of athletes and nonathletes.
* 10% condition The samples represent less than 10% of all possible non-athletes and less than 10% of all possible athletes who could be admitted to State U. from Gossett High School.
* Nearly Normal condition The histograms show that both sets are unimodal and roughly symmetric.

Because the conditions are satisfied, it is appropriate to model the sampling distribution of the difference in the means with a Student's t-model, and we will perform a two-sample t-test.
 = 16		  = 24.75		 = 2.84
 = 7		  = 21.86		 = 3.29
SE( - ) =  =  =  = 1.432
The observed difference is  -  = 24.75 - 21.86 = 2.89
t =  =  = 2.02
The sampling distribution model has 10.13 degrees of freedom. 

Since the P-value is low, we reject the null hypothesis. There is evidence of a difference between the mean ACT scores for non-athletes and athletes.