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.

(a) 95% confidence interval for the population mean body temperature for healthy female is between a lower limit of 98.21 °F and an upper limit of 98.57 °F.

(b) The average is less than 98.6 °F

(c) Yes

Step-by-step explanation:

(a) Confidence interval = mean + or - Margin of Error (E)

mean = 98.39 °F

sd = 0.743 °F

n = 65

degree of freedom = n - 1 = 65 - 1 = 64

confidence level = 95%

t- value corresponding to 64 degrees of freedom and 95% confidence level is 1.9976.

E = t×sd/√n = 1.9976×0.743/√65 = 0.18 °F

Lower limit = mean - E = 98.39 - 0.18 = 98.21 °F

Upper limit = mean + E = 98.39 + 0.18 = 98.57 °F

95% confidence interval is between 98.21 °F and 98.57 °F.

(b) The average is less than 98.6 °F. The lower limit 98.21 °F and the upper limit 98.57 °F are both less than 98.6 °F

(c) It was valid to use the t-distribution approach to find the confidence Interval beci it gives a range of values for the population mean body temperature for healthy female.