## Hypothesis Testing for a Population Mean Forum

The average body temperature for healthy adults is 98.6 °F. Is this statement true? Do all healthy people have exactly the same body temperature? A study was conducted a few years go to examine this belief.

The body temperatures of n = 130 healthy adults were measured (half male and half female). The average temperature from the sample was found to be x̄ = 98.249 with standard deviation s = 0.7332.

Do these statistics contradict the belief that the average body temperature is 98.6? If the true average temperature is indeed 98.6 °F and we obtain a sample of n = 130 healthy adults, we would not expect the sample mean to come out exactly equal to 98.6 °F. We observed x̄ = 98.249- can this deviation from 98.6 be explained by chance or is it unlikely we would observe a value this different from 98.6?

Two people debating this issue could come to different conclusions.

Using the methods introduced in this module, discuss how you would determine if the data contradicts the hypothesis that the average body temperature is 98.6°F

First of all the sample of the body temperatures of n = 130 healthy adults is just a sample from the population of the body temperatures of all the living humans. And we know that there is always some variation in the sampling thus the sample average can vary from the population average.

This imply that observing the sample mean x̄ = 98.249 does not cancel out the chance that the population mean is 98.6 °F. The correct procedure would be using a hypothesis test to support the claim.

Note that here the sample size is large and it is a one sample test for mean and thus a Z test would be most appropriate.

The null and alternative hypotheses are,

H0: µ = 98.6 and H1: µ ≠ 98.6

Test Statistic = -5.458

The critical values at 5% significance level are ±1.96.

We can see that the test statistic is falling in the rejection region thus we are rejecting the null hypothesis at 5% significance level in conclusion that the obtained sample results is providing enough evidence that the population mean body temperature is significantly different from 98.6 °F at 5% significance level.

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