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

Question

It has long been stated that the mean temperature of humans is 98.6 degree F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degree F 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 97.8 F and a sample standard deviation of 0.5 degree F. (a) Using the classical approach, judge whether the mean temperature of humans is less than 98.6 degree F at the alpha = 0.01 level of significance. (b) Approximate P-value. (a) Choose the correct answer below. A. Reject H_0 since the test statistic is less than the critical value. B. D_0 not reject H_0 since the test statistic is less than the critical value. c. D_0 not reject H_0 since the test statistic is not less than the critical value. D. Reject H_0 since the test statistic is not less than the critical value. (b) The P-value is approximately (Round to four decimal places as needed.) Click to select your answer(s)

Explanation / Answer

Solution:

(a) Let be the population mean

Ho: = 98.6
Ha: < 98.6

The test statistic is
Z = (x-)/(s/n)
= (98.8-98.6)/(0.5/sqrt(148))
= 4.87

It is a left-tailed test.
Given = 0.01, the critical value is Z(0.01)= -2.33 (from standard normal table)
Since Z = 4.87 is greater than -2.33, do not reject Ho.
C) Do not Reject Ho, since the test statistic is not less than critical value

------------------------------------------------------------------------------------------

(b) The p-value= P(Z < 4.87) = 0 (from standard normal table)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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