2-Sample Proportion Practice

Instructions

Complete the following questions about testing differences between 2 proportions. When completed, Render the qmd file and submit the html.

A Penny Saved?

A random sample of BYU-Idaho students was surveyed and asked if they were in favor of retaining the penny as a form of currency in the United States. Out of the 116 women surveyed, 80 said that they were in favor of retaining the penny as a form of currency. Of the 137 men surveyed, 91 said that they were in favor of retaining the penny. For these questions, let group 1 represent women and group 2 represent men.

Question: Are the requirements satisfied for assuming normality? Explain.
Answer:

Regardless of whether or not the requirements are satisfied, complete the following:

Confidence Interval

Create a 95% confidence interval for the difference in the proportion of females to males who prefer to keep the penny:

Question: Interpret the confidence interval in context of the question:
Answer:

Hypothesis Test

You also want to see if there is a difference between the proportion of women who want to keep the penny and the proportion of men who want to keep the penny. Use a level of significance of \(\alpha = 0.05\).

State your null and alternative hypotheses:

\[H_0: p_{female}???p_{male}\]
\[H_a: p_{female}???p_{male}\]

Question: What is the test statistic?
Answer:

Question: What is the P-value?
Answer:

Question: Based on your decision rule, state your conclusion in context of the problem:
Answer:

Couples Retreat?

A marriage counselor conducted a study of couples, categorizing each of the couples as “communicative” or “non-communicative”. Among other things, the counselor wanted to see whether the percentage of communicative couples whose marriage ended in separation or divorce was the same as the percentage of non-communicative couples whose marriage ended in separation or divorce.

Hypothesis Test

Construct a null and alternative hypothesis for the study:

\[H_0: \]
\[H_a: \]

Perform the appropriate analysis:

Question: What is the test statistic?
Answer:

Question: What is the P-value?
Answer:

Question: Based on your decision rule, state your conclusion in context of the problem:
Answer:

Confidence Interval

Create a 95% confidence interval for the difference in the proportion of divorces between communicative and non-communicative couples:

Question: Interpret the confidence interval in context of the question:
Answer: