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. a) State the null hypothesis. State the null hypothesis.
H0:
p > 0.13
H0:
p ≤ 0.13
H0:
p ≠ 0.13
H0:
p ≥ 0.13
b) State the alternative hypothesis.
Ha:
p ≠ 0.13
Ha:
p > 0.13
Ha:
p < 0.13
Ha:
p = 0.13
c) In words, state what your random variable P' represents.
P' represents the number of Americans who have seen or sensed angels.
P' represents the proportion of Americans who have seen or sensed angels.
P' represents the ratio of Americans who have seen or sensed angels to those who haven't.
P' represents the proportion of Americans who have not seen or sensed angels.
d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)
e) 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.)
f) What is the p-value? (Round your answer to four decimal places.)
g) 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.)
h) Give three reasons why the two polls might give different results.