A local radio station advertises that at least 30% of listeners in its reception area tune into its daily news broadcasts. A company that is considering advertising on this radio station in its news slot wants to test the validity of this statement. They will place adverts in the news timeslots if the radio station's statement can be verified. The company conducted a telephone survey of 400 randomly selected listeners to test the radio station's statement. If 106 listeners in the survey indicated that they tuned into the local radio's news broadcasts, should the company place adverts in the radio station's news timeslots?
(a) Recommend a course of action to the management of the company, based on the results of a hypothesis test for a single proportion conducted at the 5% level of significance.
(b) Compute the p-value of the test statistic using Excel's NORMSDIST function. Interpret the p-value for the management of the company.
(c) Confirm the p-value found in (b) by using Excel's NORMDIST function.