It has long been stated that the mean temperature of humans is 98.6 degreesF. Ho

Question

It has long been stated that the mean temperature of humans is 98.6 degreesF. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degreesF. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 700 measurements. The sample data resulted in a sample mean of 97.6 degreesF and a sample standard deviation of 0.6 degrees F. (a) Using the classical approach, judge whether the mean temperature of humans is less than 98.6 degreesF at the alpha equals0.01 level of significance. (b) Approximate the P-value. LOADING... Click here to view the t-Distribution Area in Right Tail. (a) Choose the correct answer below. A. Reject Upper H 0 since the test statistic is not less than the critical value. B. Reject Upper H 0 since the test statistic is less than the critical value. C. Do not reject Upper H 0 since the test statistic is less than the critical value. D. Do not reject Upper H 0 since the test statistic is not less than the critical value.

Explanation / Answer

The sample data resulted in a sample mean of 97.6 degreesF and a sample standard deviation of 0.6 degrees F.

given that

xbar = 97.6

sd = 0.6

n = 148

and mu = 98.6

now we know that

t = (xbar-mu)/(sd/sqrt(n))

= (97.6-98.6)/(0.6/sqrt(148)) = -20.27

Now the df = n - 1

= 148-1 = 147

so we check the t table for df = n-1 = 147

and alpha = 0.01

we see

t-value (right-tail): 2.351

please note that this is a 1 tail test as we are interested in the "less" part

as the critical value is not less than the calclulated value , hence we fail to reject the null hypothesis and conclude that

Do not reject Upper H 0 since the test statistic is less than the critical value, choice C

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.