Question: When shall we call you? Carry out the significance test called for in Exercise in all detail. Show the five steps of the test (hypotheses, sampling distribution, data, P-value, conclusion) clearly.
Exercise: When shall we call you? Suppose we knew that 57% of all calls made by sample surveys on weekday mornings are answered. We make 2454 calls to randomly chosen numbers during weekday evenings. Of these, 1840 are answered. Is this good evidence that the proportion of answered calls is higher in the evening?
(a) State the hypotheses to be tested.
(b) If your null hypothesis is true, what is the sampling distribution of the sample proportion p^? Sketch this distribution.
(c) Mark the actual value of p^ on the curve. Does it appear surprising enough to give good evidence against the null hypothesis?