Two random samples are taken, one from among first-year wwu students and the other from among fourth-year wwu students. both samples are asked if they favor modifying the cafeteria plan. a summary of the sample sizes and number of each group answering yes" is given below: is there evidence, at an alpha = 0.05 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. the value of the test statistic is x_text^2 = the critical value is: your decision for the hypothesis test:

The question is incomplete. This is the missing part n1= 95, x1=45 n2=95 x2=63.

The hypothesis for the question :

H0: p1=p2

H1: p1 not equal to p2

The point estimate of the population proportion for the first year

P1 = 64/92=0.6957

P2= 71/96=0.7396

The test statistic is given by:

Z= (p1-p2)/√p cap(1 - p cap) ×(1/n1 +1/n2)

P1= 0.6957. P2= 0.7396. P cap = (64+71)/(92+96)

=0.7181

The test statistic z= - 0.6687

b) The rejection region for the test statistic is the area where the p value is less than the alpha level.(0.05).

c) the p value is 0.2514

d) since the p value is greater than the alpha level (0.05) we accept the null hypothesis and conclude that there is no difference in proportions between first-years and fourth-years.