16 of 28 (12 complete) Question: 10 pts Question Help as long been stated that t

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16 of 28 (12 complete) Question: 10 pts Question Help as long been stated that the mean temperature of humans is 98.6 F. However,two researchers currently involved in the subject thought that e mean temperature of humans is less than 98.8 F. They measured the temperatures of 148 healthy aduits 1 to 4 times daily for 3 days taining 600 measurements. The sample data resu ed in a sample mean o 97.9°F and a sa ple standard deviation of 6 F Using the classical approach, judge whether the mean temperature of humans is less than 986 F at the a-001 level of significance. b)Approximate the P-value BClick here to view the t-Distribution Area in Right Tail (a) Choose the correct answer below O A. Reject Ho since the test statistic is not less than the critical value O B. Do not reject Ho since the test statistic is less than the critical value. O c. Do not reject Ho since the test statisticis not less than the critical value 0 D. Reject Ho since the test statistic is less than the critical value. b) The P-value is approximately (Round to fur decimal places as needed ) Click to select your answerts) enovO Esc 2 3 4 6

Explanation / Answer

The appropriate hypotheses for the testing are:

Null Hypothesis, H0 : µ = 98.6

Alternate Hypothesis, H1 : µ < 98.6

The test statistic = (97.9-98.6)/(0.6/sqrt(600)) = -28.5774

Critical t-value for a left tailed t-distribution corresponding to alpha =0.01 is about -2.33259 (This can be found in MS Excel using the function =T.INV(0.01,599). Here, 599 is the degrees of freedom.

Since our test statistc is less than the critical t-value, we can reject the Null hypothesis.

So, Reject H0 since the test statistic is less than the critical value.

Option D shown in the question is correct.

The p-value corresponding to the test statistic of -28.5774 is approximately 0. This can be calculated in MS Excel as =T.DIST(-28.5774,599,TRUE) and the value obtained is 2.8665 x 10-114.

Rounded to 4-decimalplaces as asked in the question, the p-value is 0.

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