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# Confidence Interval III

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A chain of launderettes is investigating the lifetime of the washing machines that they use, measured in the number of washes completed before they need repairing. There are a number of machines used throughout their branches that have been installed at different times with each one having the number of completed washes recorded. To sample the lifetime of the washing machines the most recent 125 machines that have failed had their lifetimes recorded. This sample had a mean lifetime of 3124 hours and a variance of 2017.

a) Calculate a 95% confidence interval for the average lifetime of the washing machines that the company uses.

b) Calculate the sample size required to reduce the margin of error for a 95% confidence interval down to 7 (i.e. E = 7).

Please do not use excel functions. I would like to see clear workings and commentary for calculations.

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#### Solution Preview

a) At 95% level and df=n-1=125-1=124, the critical value is 1.9793 from t table.
So 95% confidence interval ...

#### Solution Summary

The solution gave detailed steps on computing the confidence interval. All formula and calculations are shown and explained.

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## Confidence interval estimation

The data that you will be using for this exercise came from a survey of two insurance carriers.

The first carrier (C1) was compared against the second competitor (C2). The insurance company management team
wants to know how Carrier 1 compared to the second carrier. Data from 159 respondents are included.

All of the 5 questions are rated on a scale of 1 to 5, with 1 being "much worse" and 5 being "much better"

1. Graph the 5 main survey variables in a histogram. For each graph you are going to graph out the data values, grouped by responses. You should have categories that are the responses 1-5. You should have 5 histograms, and on each, display both the C1 and C2 data on the same graph. What can you see from these graphs?

2. Create 95% confidence intervals for the mean for the 5 survey variables on Carrier 1.

3. Perform 5 t-tests on the data comparing C1 to C2 on each of the 5 questions. Indicate which of the 5 variables has a difference between C1 and C2.

4. Interpret the data and write an brief (2 paragraph) executive summary to C1 management describing your findings.

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