A simple random sample of epicenter depths of 51 earthquakes has a mean of 9.808 kilometers (km) and a standard deviation of 5.013 km

A simple random sample of epicenter depths of 51 earthquakes has a mean of 9.808 kilometers (km) and a standard deviation of 5.013 km. Determine the critical value of t and the margin of error, and then construct the 95% confidence interval estimate of the mean epicenter depth of all earthquakes.

Solutions

Expert Solution

Given that

n = 51, x̅ = 9.808 km S.D = S = 5.013 km

d.f = n – 1 = 50

α = 1-95% = 1-0.96 = 0.05

tα/2 d.f = 2.01

Margin of error = critical value × s/√n

= 2.01 × 5.013/√51

M.E = 1.4099

∴ 95% confidence interval for population mean is

[x̅ ± M.E] = [9.808 ± 1.4099]

[8.3981, 11.2179]

∴95% confidence interval estimate of the mean epicenter depth of all earthquake lies between 8.3981 and 11.2179.

Junaid answered 1 year ago

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