# 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.

Sample Statistics Problems

1. A survey of 400 people who took vacations revealed that 242 of them flew to their destination. Give a 95% confidence interval for the percentage of all people who fly when they take a trip. Does it appear statistically correct to conclude that more than 50% of all people who take vacations will fly to their destination? Why or why not?

2. Suppose you want to estimate the percentage of adults who fly to their vacation destination and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 95% confidence level. What size sample is required?--(assume that no estimate of "p-hat" is known.)

3. The average systolic blood pressure readings from a random sample of 100 people is 123.4 (assume a population standard deviation of 15.6). Based upon a desired 99% confidence level, determine the margin of error E in this sample statistic and then give the associated confidence interval.

4. You need to estimate the mean useful life of a certain brand of light bulb to within 20 hours with 98% confidence. Previous studies indicate that the standard deviation for the light bulb is 40 hours. How many observations should your sample contain to meet this desired level of accuracy?

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