How do you construct a 95% confidence interval?

You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you randomly select 40 repair costs and find the mean to be $100. The sample standard deviation if $17.50. How do you construct a 95% confidence interval for the population mean repair cost?

1 Answer
SCooke
Apr 23, 2018

[94.58, 105.42][94.58,105.42]

Explanation:

Given the mean, standard deviation, the number of samples and the desired confidence interval, the interval is calculated from the following formula:

barx "+/-" (z xx (sigma/sqrt(n)))¯x+/-(z×(σ√n))

where z is from the standard distribution tables (in the reference), and is 1.96 for a CI of 95%.
100 "+/-" (1.96 xx (17.50/sqrt(40)))100+/-(1.96×(17.50√40))
100"+/-" 5.42100+/-5.42 or

[94.58, 105.42][94.58,105.42]

http://www.dummies.com/education/math/statistics/how-to-calculate-a-confidence-interval-for-a-population-mean-when-you-know-its-standard-deviation/

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