In this question we are conducting a hypothesis test. Assume that the data described meet the appropriate success-failure conditions.

In a random sample of 500 adults in the U.S., 60.2% owned their homes. Conduct a hypothesis test in which you test whether these data provide evidence that a majority or minority of U.S. adults own their homes, as opposed to the population of U.S. adults being split equally among homeowners and non-homeowners (50%). Make sure to show any and all work clearly and in a well-organized way and to use complete sentences to answer questions when appropriate.

a) What are the null and alternative hypotheses? Use mathematical notation to define the hypotheses (for examples of this type of notation, review the module on hypothesis tests).

b) What type of test statistic will you need to use? What is the value of that test statistic?

c) What is the p-value that corresponds to your test statistic for this hypothesis test?

d) Conclude your hypothesis test. Using the 95% significance level as your criteria, do you reject or fail to reject your null hypothesis, why or why not? What does the conclusion to the hypothesis test mean substantively?