Mathematics Question

DISCUSSION

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.

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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 = 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 = 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.

instructor notes

This discussion is a bit more technical and there is a definite correct answer. I will outline the procedure here and leave the calculations and the conclusion to you.

At the start of the third paragraph we can find the claim of this hypothesis test, that the average body temperature is equal to 98.6. When the claim uses ‘equal to’ type language we will use an alternative hypothesis of ‘not equal to’. So our hypotheses about population average body temperature are:

H0: mu = 98.6

Ha: mu not equal to98.6

Since this is a hypothesis test about a population mean and the population standard deviation is unknown we will use t statistics for the critical value and the test statistic.

The first question for you to answer is what direction is this test? Look at the alternative hypothesis for the answer.

Then, we are not given a significance level for this test. It is up to you to pick your own. Normally we stick with alpha = 0.01 or alpha = 0.05.

Once that is decided you will be ready to find the critical value. We will use a T.INV formula, but the exact inputs will depend on the direction of the test and the level of alpha you picked. Once you do calculate it the next step is to describe the rejection region. In other words, what parts of the bell curve will cause us to reject the null hypothesis if the test statistic is there?

Now it is time to calculate the test statistic. The formula for this is:

t equals fraction numerator top enclose x minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction

All of these variables are given in the directions, but notie that the population parameter mu is given in the null hypothesis.

Finally, we are able to state whether or not we reject the null hypothesis. Be sure to support your decision by including a comparison of the test statistic and critical value. Then the last step is to restate the concludion in terms of the original claim, does the evidence support the claim that the average temperature is equal to 98.6?

I hope this helps, but don’t be afraid to give it a try and make mistakes. We have all week to work it out. If you want to use any mathematical symbols use the square root sign button on the toolbar at the top of the discussion box.

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