Question

A poll done for an organization found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 78 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent's survey, would you agree with the organization's poll? Conduct a hypothesis test at the 5% level.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1. State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

2. What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

3. What is the p-value? (Round your answer to four decimal places.)

4. Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Keep in mind that a negative value wouldn't be practical in this situation. Round your answers to four decimal places.)

5. Give three reasons why the two polls might give different results. (Select all that apply.)

A. The polls may have been worded differently.

B. One of the polls may have included more people wearing glasses.

C. One of the polls may have been conducted later in the day.

D. One of the polls may have included more people who consider themselves religious.

E. Random chance could account for some of the difference.

Answer 1