Question

In: Statistics and Probability

4) You are hired by a cell phone provider to determine the number of times per...

4) You are hired by a cell phone provider to determine the number of times per day their customers interact with their smartphone. You take a random sample of 25 customers and find the average number of interactions to be 75 times per day with a sample standard deviation of 5.

4 a. If you decide to construct a confidence interval for the population mean number of interactions, what distribution would you use and why? ________________________________________________________________________________

________________________________________________________________________________ ________________________________________________________________________________

b. Construct a 99% confidence interval estimate for the population mean number of interactions.

c. What is the margin of error for the confidence interval you found in part b?

d. A representative for the cell phone provider told you they believe the mean number of interactions per day was 83. What would you say to the company representative? Explain.

__________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________

Solutions

Expert Solution

4. a. In order to construct a confidence interval for the population, we need to use normal distribution. Since, the population standard deviation is unknown, we use t-distribution.

b. The 99% confidence interval of the mean number of interactions = [, ], where, = 75, s = 5, n = 25

Thus, 95% C.I. = [75 - 2.797, 75 + 2.797] = [72.203, 77.797]

c. The margin of error of the interval = = 2.797

d. Since, 83 is not contained in the 99% confidence interval, the estimate of the cell phone provider is not correct.

orchestra answered 2 years ago
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