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------------------------------------------------ It is commonly believed that the average body temperature for humans is 98.6 degrees F. A study was conducted in which a group of healthy adults had their temperature measured 1 to 4 times daily for 3 days, resulting in 175 temperature measurements. The sample mean temperature was 98.2 degrees F, with a sample standard deviation of 0.7 degrees F.

Construct a 95% confidence interval for the mean body temperature of humans. Show all work. Round the margin of error and interval bounds to 2 decimal places.

Answer :

The 95% confidence interval estimate of the population mean is 98.10< μ < 98.30.

Given that

sample mean = ~x = 95.2

sample standard deviation = s = 0.7

sample size = n = 175

Degrees of freedom = d.f = n - 1 = 175 - 1 = 174

αt /2,d.f = 1.974.

The explanation for step 1

At 95% confidence level

α= 1-0.95% =1-0.95 =0.05

α /2=0.05/ 2= 0.025

αt /2,d.f = t0.025,174 = 1.974

αt /2,d.f = 1.974

The explanation of Step 2

Margin of error = E = t/2,df x (s /Vn ) = 1.974 x ( 0.7/ V175) = 0.10

Margin of error = E = 0.10

The 95% confidence interval estimate of the population mean is,

~x- E < μ < ~x + E

98.2 - 0.10< μ < 98.2 + 0.10

98.10< μ < 98.30

Margin of error = E = 0.10

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