Question

It has long been stated that the mean temperature of humans is 98.6degreesF. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6degreesF. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3​ days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3degreesF and a sample standard deviation of 0.9degreesF. Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6degreesF at the alpha=0.01 level of significance.

State the hypotheses.

Upper H 0H0​:▼▼ 98.6 F

Upper H 1H1​:▼▼ 98.6 F

Find the test statistic.

t0=? ​(Round to two decimal places as​ needed.)

The​ P-value is ? ​(Round to three decimal places as​ needed.)

What can be​ concluded?

A. RejectUpper H0 since the​ P-value is less than the significance level.

B. Reject Upper H0 since the​ P-value is not less than the significance level.

C.Do not reject Upper H0 since the​ P-value is less than the significance level.

D. Do not reject Upper H0 since the​ P-value is not less than the significance level.

Answer 1

Solution :

= 98.6

= 98.3

s = 0.9

n = 61

This is the left tailed test .

The null and alternative hypothesis is

H0 :   = 98.6

Ha : < 98.6

Test statistic = t

= ( - ) / s / n

= (98.3 - 98.6) /0.9 / 61

= -2.60

P (t<-2.60 ) = 0.0059 = 0.006

P-value = 0.006

= 0.01  

0.006 < 0.01

A. RejectUpper H0 since the​ P-value is less than the significance level.