Question

1. 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 20 customers and find the mean average number of interactions to be 45 times per day with a sample standard deviation of 8.
   

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

2. Construct a 95% confidence interval (to 2 decimal places) estimate for the population mean number of interactions.

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

4. A representative for the cell phone provider told you they believe the mean number of interactions per day was 52. What would you say to the company representative? You must explain your answer to receive credit.

Answer 1

(a) The t-distribution will be used because we have the sample standard deviation and the sample size is less than 30.

(b) The 95% confidence interval is:

= 45 2.09*(8/20)

= 41.26, 48.74

(c) The margin of error = 2.09*(8/20) = 3.74

(d) Since the confidence interval does not contain 52, we can say that the mean number o interactions per day was not 52.

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