Question

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=84,n2=88,x1=43x2=38

Is there evidence, at an ?=0.08 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (??,a) is expressed (-infty, a), an answer of the form (b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject H0.
B. Reject H1.
C. Reject H0.
D. Do Not Reject H1.

2) 1. In a study of red/green color blindness,

550 men and 2150 women are randomly selected and tested. Among the men, 50have red/green color blindness. Among the women, 4 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
The test statistic is  
The p-value is  
Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.05% significance level?

A. No
B. Yes

2. Construct the 95% confidence interval for the difference between the color blindness rates of men and women.
<(p1?p2)<  

Which of the following is the correct interpretation for your answer in part 2?
A. There is a 95% chance that that the difference between the rates of red/green color blindness for men and women lies in the interval
B. We can be 95% confident that the difference between the rates of red/green color blindness for men and women lies in the interval
C. We can be 95% confident that that the difference between the rates of red/green color blindness for men and women in the sample lies in the interval
D. None of the above

Answer 1

Result:

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=84,n2=88,x1=43x2=38

Is there evidence, at an ?=0.08 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic: 1.0518

Note: For the next part, your answer should use interval notation. An answer of the form (??,a) is expressed (-infty, a), an answer of the form (b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic: (-infty, -1.7507)U(1.7507, infty).

C. The p-value is 0.2929

D. Your decision for the hypothesis test:

Answer: A. Do Not Reject H0.
B. Reject H1.
C. Reject H0.
D. Do Not Reject H1.

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.08
Group 1
Number of Items of Interest	43
Sample Size	84
Group 2
Number of Items of Interest	38
Sample Size	88
Intermediate Calculations
Group 1 Proportion	0.511904762
Group 2 Proportion	0.431818182
Difference in Two Proportions	0.08008658
Average Proportion	0.4709
Z Test Statistic	1.0518
Two-Tail Test
Lower Critical Value	-1.7507
Upper Critical Value	1.7507
p-Value	0.2929
Do not reject the null hypothesis

2) 1. In a study of red/green color blindness,

550 men and 2150 women are randomly selected and tested. Among the men, 50have red/green color blindness. Among the women, 4 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
The test statistic is  13.3112
The p-value is   0.0000
Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.05% significance level?

A. No
Answer: B. Yes

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	50
Sample Size	550
Group 2
Number of Items of Interest	4
Sample Size	2150
Intermediate Calculations
Group 1 Proportion	0.090909091
Group 2 Proportion	0.001860465
Difference in Two Proportions	0.089048626
Average Proportion	0.0200
Z Test Statistic	13.3112
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0000
Reject the null hypothesis

2. Construct the 95% confidence interval for the difference between the color blindness rates of men and women.
0.0650 <(p1?p2)<  0.1131

Which of the following is the correct interpretation for your answer in part 2?
A. There is a 95% chance that that the difference between the rates of red/green color blindness for men and women lies in the interval
Answer: B. We can be 95% confident that the difference between the rates of red/green color blindness for men and women lies in the interval
C. We can be 95% confident that that the difference between the rates of red/green color blindness for men and women in the sample lies in the interval
D. None of the above

CI = p1-p2 ± z*se

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	95%
Intermediate Calculations
Z Value	-1.9600
Std. Error of the Diff. between two Proportions	0.0123
Interval Half Width	0.0241
Confidence Interval
Interval Lower Limit	0.0650
Interval Upper Limit	0.1131