Part 1A credit card company operates two customer service centers. Callers to the service centers dial a single​ number, and a computer program routes callers to the center having the fewest calls waiting. As part of a customer service review​ program, the credit card center would like to determine whether the average length of a call​ (not including hold​ time) is different for the two centers. The managers of the customer service centers are willing to assume that the populations of interest are normally distributed with equal variances. Suppose a random sample of phone calls to the two centers is selected and the results that were reported are shown below. Complete parts a and b.[table] | Center A | Center B Sample Size | 115115 | 140140 Sample Mean​ (seconds) | 57.657.6 | 66.766.7 Sample St. Dev.​ (seconds) | 6.46.4 | 6.46.4 [/table] Part 1a. Using the sample​ results, develop an 8080​% confidence interval estimate for the difference between the two population means. Let sample 1 be the sample from Center A and let sample 2 be the sample from Center B.[input]enter your response here less than or equals≤left parenthesis mu 1 minus mu 2 right parenthesisμ1−μ2less than or equals≤[input]enter your response here ​(Round to two decimal places as​ needed.)多项填空题

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Consider two independent samples.  One sample has size 100 and comes from a distribution with mean  𝜇 1 and standard deviation  𝜎 1 , and we observe a sample mean of 5 and a sample standard deviation of 2.  The other sample has size 50 and comes from a distribution with mean  𝜇 2 and standard deviation  𝜎 2 , and we observe a sample mean of 10 and a sample standard deviation of 3. Assuming  𝜎 1 = 𝜎 2 , what critical value should we use to form an 80% confidence interval for 𝜇 1 − 𝜇 2 ?

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