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In: Statistics and Probability

A poll done for an organization found that 13% of Americans have seen or sensed the...

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 tdf where df is the degrees of freedom.)

2. 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.)

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