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: is there evidence, at an 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 is expressed (-infty, a), an answer of the form is expressed (b, infty), and an answer of the form 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. reject . b. do not reject . c. reject . d. do not reject .

Answer 1

This question involves a hypothesis test to compare two independent population proportions of first-year and fourth-year university students' opinions on modifying the honor code, using steps that include defining hypotheses, calculating statistics, and making decisions based on p-value and significance level.

Step-by-step explanation:

The question involves conducting a hypothesis test for the difference in proportions between two groups, in this case, first-year students and fourth-year students at a public university, concerning their views on modifying the student honor code. It requires knowledge of statistics, particularly in conducting tests for comparing two independent population proportions. The random variable for such a study would typically be the number of yes responses in each sample, and the test itself would involve the following steps:

1. Define the null and alternative hypotheses.
2. Calculate the pooled proportion if necessary.
3. Determine the value of the standardized test statistic.
4. Identify the rejection region based on the chosen level of significance.
5. Compute the p-value.
6. Make a decision to reject or not reject the null hypothesis based on the comparison of the p-value and alpha level.

For example, if comparing proportions of households with cable service in two communities, we would utilize the null hypothesis that there is no difference in proportions and an alternative hypothesis that there is a difference. We would calculate the pooled proportion based on the data provided for each community.