Question

An insurance claims department asserts that it responds to the customer claims within 15 days. A simple random sample of 40 claims show a sample means of 27 days for the response time. The standard deviation of this sample is 6 days. a) Construct a 95% confidence interval for the mean response time for all the claims. b) Does this interval contain the value 15 of days?

Answer #1

**Answer:**

Based on the given information:

Claim: Insurance claim department responds to customer claim within 15 days

- Sample size (n) = 40
- Sample mean = 27 days
- Sample Standard deviation (s) = 6 days

**a) Construct a 95% confidence interval for the mean
response time for all the claims.**

In this case, since population standard deviation is not known, therefore, t-statistics will be used to build confidence interval.

Therefore, a 95% confidence interval for the mean response time is 25.081 - 28.920

**b) Does this interval contain the value 15 of
days?**

- No, this interval doesnot contain the value of 15 days

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