In a city, a radio programme hosted by Tao has long been very popular. Tao has just retired and gone to London, and Wing will be the new host of the programme. Let p be the proportion of residents in the city who are regular listeners. It is known that p= 0.5 before Tao retired. A market analyst is planning to conduct a test to examine if p will be changed one month after Wing has become the new host. The analyst will conduct the test by interviewing a random sample of 100 residents. Let X be the number of regular listeners of the programme. The analyst will reject the null hypothesis if X is smaller than 41 or greater than 59. (a) Calculate the size of the test. (b) Suppose that the true value of p is 0.38. Calculate the probability of committing а Туре II error. (c) Using Excel, plot a graph of the power function.

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In a city, a radio programme hosted by Tao has long been very popular. Tao has just
retired and gone to London, and Wing will be the new host of the programme. Let
p be the proportion of residents in the city who are regular listeners. It is known that
p= 0.5 before Tao retired. A market analyst is planning to conduct a test to examine
if p will be changed one month after Wing has become the new host.
The analyst will conduct the test by interviewing a random sample of 100 residents.
Let X be the number of regular listeners of the programme.
The analyst will reject the null hypothesis if X is smaller than 41 or greater than 59.
(a) Calculate the size of the test.
(b) Suppose that the true value of p is 0.38. Calculate the probability of committing
a Type II error.
(c) Using Excel, plot a graph of the power function.
Transcribed Image Text:In a city, a radio programme hosted by Tao has long been very popular. Tao has just retired and gone to London, and Wing will be the new host of the programme. Let p be the proportion of residents in the city who are regular listeners. It is known that p= 0.5 before Tao retired. A market analyst is planning to conduct a test to examine if p will be changed one month after Wing has become the new host. The analyst will conduct the test by interviewing a random sample of 100 residents. Let X be the number of regular listeners of the programme. The analyst will reject the null hypothesis if X is smaller than 41 or greater than 59. (a) Calculate the size of the test. (b) Suppose that the true value of p is 0.38. Calculate the probability of committing a Type II error. (c) Using Excel, plot a graph of the power function.
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