Question

Normal (or average) body temperature of humans is often thought to be 98.6° F. Is that number really the average? To test this, we will use a data set obtained from 65 healthy female volunteers aged 18 to 40 that were participating in vaccine trials. We will assume this sample is representative of a population of all healthy females.

A.  The mean body temperature for the 65 females in our sample is 98.39° F and the standard deviation is 0.743° F. The data are not strongly skewed. Use the Theory-Based Inference applet to find a 95% confidence interval for the population mean body temperature for healthy female

B. Based on your confidence interval, is 98.6° F a plausi- ble value for the population average body temperature or is the average significantly more or less than 98.6° F? Explain how you are determining this.

C.  In the context of this study, was it valid to use the theory-based (t-distribution) approach to find a confi- dence interval? Explain your reasoning.

Answer 1

We want to test the claim "Is 98.6 really the Normal (or average) body temperature of humans?"

Let's write the null hypothesis ( H₀ ) and alternative hypothesis (H_a)

$H_{0}:\mu = 98.6$

$H_{a}:\mu \neq 98.6$

Let's write the given information

n = sample size = 65

$\bar x$ = sample mean = 98.39

s = sample standard deviation = 0.743

From the alternative hypothesis the given test is two tailed test

Hypothesis testing

Here population standard deviation is not given and we use sample standard deviation(s) instead of population

standard deviation . Also sample size is sufficiently large( >= 30) so we can used one sample t test

Using minitab we get following result

The command is Stat>>>Basic Statistics >>1 sample t...

Select summary Statistics

Look the following image:

-Sample t (fest and Contfidence Interval) 1-Sample tTest and Interval) C Samples in columns: Summarized data Sample size: Mean: Standard deviation: 0.743 65 98.39 Г Perform hypothesis test Hypothesized mean: Graph.... Optons.. Select Help OK

Then click on Option

Confidence level = 95

Alternative " not equal"

then click on Ok

We get the following output

One-Sample T Mean StDev SE Mean 95% CI 65 98.3900 0.7430 0.0922 (98.2059, 98.5741)

From the above output the 95%  confidence interval for the population mean body temperature for healthy female is (98.2059, 98.5741)

B) From the above confidence interval  the population average body temperature or is the average significantly less than 98.6° F because the upper limit of the confidence interval is less than 98.6° F

C) Yes because the sample size is large( > 30) so that we can used t distribution approach to find the confidence interval for population mean.