A technician randomly sampled repair logs for computers at a university. He wanted to find out how many times the computers were repaired. The proportion of computers that were repaired more than three times in the last two years was 0.24, with a margin of error of 0.03. Construct a confidence interval for the proportion of university computers that were repaired more than three times in the last two years.

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-29T20:56:44+02:00

Answer: [tex](0.21,\ 0.27)[/tex]

Step-by-step explanation:

The confidence interval estimate for the population proportion is given by :-

[tex]\hat{p}\pm ME[/tex], where [tex]\hat{p}[/tex] is the sample proportion of success and ME is the margin of error.

Given : The proportion of computers that were repaired more than three times in the last two years : [tex]\hat{p}=0.24[/tex]

Margin of error : [tex]ME=0.03[/tex]

Now, the confidence interval estimate for the population mean will be :-

[tex]0.24\pm0.03=(0.24-0.03,\ 0.24+0.03)=(0.21,\ 0.27)[/tex]

Hence, the 98% confidence interval estimate for the population mean using the Student's t-distribution = [tex](0.21,\ 0.27)[/tex]