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Statistics - 95% error margin and 98% confidence interval

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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 Summary

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

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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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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