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=82,n2=99,x1=56x2=65

Is there evidence, at an α=0.03 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:
B. The rejection region for the standardized test statistic:
C. The p-value is:_____

Answer 1

To test whether there is a difference in proportions between first-year and fourth-year students, we can use a hypothesis test for comparing two independent population proportions and calculate the standardized test statistic and p-value.

Step-by-step explanation:

To test whether there is a difference in proportions between first-year and fourth-year students, we can use a hypothesis test for comparing two independent population proportions. The null hypothesis is that there is no difference in proportions, while the alternative hypothesis is that there is a difference in proportions. We can calculate the standardized test statistic and compare it to the critical value to determine if there is enough evidence to reject the null hypothesis. In this case, the standardized test statistic is calculated as:

Z = ((p1 - p2) - 0) / sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

where p1 and p2 are the proportions of first-year and fourth-year students who favor modifying the Honor Code, and n1 and n2 are the sample sizes for each group. The rejection region for the standardized test statistic can be determined using a Z-table or a statistical software. Finally, the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. We can compare the p-value to the significance level (α) to make a decision on whether to reject or fail to reject the null hypothesis.