3. -12.5 points My Notes Ask Your Teacher A poll done for an organization found

Question

3. -12.5 points My Notes Ask Your Teacher 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 73 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.) TE Part (a) Part (c) E Part (b) State the null hypothesis. State the alternative hypothesis n words, state what your random variable P represents. O Ho: p 0.13 P represents the proportion of Americans who have seen or sensed angels. Ha: p

Explanation / Answer

Part a)

Ho: p 0.13

Part b)

Ha: p < 0.13

Part c)

P represents the proportion of Americans who have seen or sensed Angel.

Part d)

Z-distribution

Part e)

z = (p^ - P)/sqrt ((P*(1-P))/n)

p^ = 2 / 73 = 0.0274

P = 0.13

n = 73

z = (0.0274 -0.13)/sqrt((0.13*(1-0.13))/73)

z = -2.61

p-value = P (z < -2.61 ) = 0.0045

if Ho is true, then there is a chance equal to the p-value that the sample ratio is not 2 out of 73 or more.

Part h)

Alpha = .05

Decision: reject the null hypothesis

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