# Statistics - 95% error margin and 98% confidence interval

1. A company wishing to improve its customer service collected hold times from 75 randomly selected incoming calls to its hot line that were put on hold. These calls had sample mean hold time = 3.4 minutes and s = 2.3 minutes. Is the claim that μ > 3.0 minutes substantiated by these data? Test with α = .05.

8.95 A random sample of 2000 persons from the labor force of a large city are interviewed, and 175 of them are found to be unemployed.

(a) Estimate the rate of unemployment based on the data.

(b) Establish a 95% error margin for your estimate.

(c) compute a 98% confidence interval for the rate of unemployment.

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#### Solution Preview

1. A company wishing to improve its customer service collected hold times from 75 randomly selected incoming calls to its hot line that were put on hold. These calls had sample mean hold time = 3.4 minutes and s = 2.3 minutes. Is the claim that μ > 3.0 minutes substantiated by these data? Test with α = .05.

Solution. Denote by μ the mean hold time.

Null hypothesis H0: μ =3

Alternative hypothesis Ha: μ >3

Note that xbar=3.4, s=2.3 and sample size n=75. So, we can compute ...

#### Solution Summary

The solution tests customer service hold times using hypothesis testing and produces a confidence interval for the mean time.