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

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 measure the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 500 measurements. The sample data resulted in a sample mean of 98.3 degree F and a sample standard deviation of 0.9 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 the P-value. (a) Choose the correct answer below. A. Do not reject H_0 since the test statistic is not less than the critical value. B. Reject H_0 since the test statistic is less than the critical value. C. Reject H_0 since the test statistic is not less than the critical value. D. Do not reject H_0 since the test statistic is less than the critical value. (b) The P-value is approximately .

Explanation / Answer

for 0.01 level of significance ; critical value of t =-2.3263

for 500 sample size ; std error =std deviatrion/(n)1/2=0.0402

hence test stat t=(X-mean)/std errror =(98.3-98.6)/0.0402=-7.4627

a) Reject Ho since test stat is less then critical value ; option B

b) p value =0.0000

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