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A meteorologist who samples 13 thunderstorms found that the average speed at which they travelled across a certain state was 15 miles per hour. The standard deviation of the sample was 1. 7 miles per hour. If you find the 99% confidence interval of the mean, what is the margin of error?.

Sagot :

raphealnwobi

The 99% confidence interval is within 13.8 miles per hour and 16.2 miles per hour

Confidence interval

sample size (n) = 13, mean (μ) = 15, standard deviation (σ) = 1.7

C = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.005

The z score of α/2 (0.005) is the same as the z score of (0.495) which is equal to 2.576.

The margin of error (E) is:

[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.576*\frac{1.7}{\sqrt13} =1.2[/tex]

The 99% confidence interval = mean ± E = 15 ± 1.2 = (13.8, 16.2)

The 99% confidence interval is within 13.8 miles per hour and 16.2 miles per hour

Find out more on Confidence interval at: https://brainly.com/question/15712887

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