Question

A real estate agent claims that more than 70% of retired couples living in apartments prefer apartment living over living in a detached house. To test this hypothesis, a random sample of 80 couples in a particular large apartment village are interviewed and 62 of them stated that they prefer apartment living.

(a) Test the agent’s claim. Make sure you state the null and alternative hypothesis, calculate the p-value (use the p-value method), make your decision and draw your conclusion (note that no level of significance is given in this question). Also: how much evidence is there against the null hypothesis?

(b) Calculate a 95% confidence interval for p, and make sure you give a good interpretation of the resulting interval (what does the interval mean in the context of the question).

Requirement: (If the question is a hypothesis test question)

• State your null and alternative hypothesis with the correct symbols, the correct inequality sign, and in words

• Calculate the value of your test statistic

• For classical testing, give the critical value of z or t; for the p-value method, calculate the p-value (as an exact value OR as a range)

• Make your decision at the stated level of significance; if no level of significance is given, you need to decide how to proceed

• Finally, you need a conclusion. The conclusion should consist of THREE things: o Is the null hypothesis plausible of not? o Is your result (the value of the sample statistic) statistically significant or insignificant? o What is the conclusion of the test in the CONTEXT of the question?

Answer 1