0.3.33 i= uestion Help t has long been stated that the mean temperature of human
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0.3.33 i= uestion Help t has long been stated that the mean temperature of humans is 986 F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 F. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 600 measurements. The sample data resulted in a sample mean of 98.4°F and a sample stardard deviation of 0.5 F a)Using the classical approach, judge whether the mean temperature of humans is less than 98.6 F at the a -0.01 level of significance. (b)Approximate the P-value. Click here to view the t-Distribution Area in Right Tail. (a) Choose the correct answer below O A. Do not reject Ho since the test statistic is not less than the critical value. B. Reject Ho since the test statistic is less than the critical value C. Do not reject Ho since the test statistic is less than the critical value. O D. Reject Ho since the test statistic is not less than the critical value (b) The P-value is approximately (Round to four decimal places as needed ) All parts 6 7 8 5 9Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 98.6
Alternative hypothesis: < 98.6
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.0204
DF = n - 1 = 600 - 1
D.F = 599
t = (x - ) / SE
t = - 9.8
tcritical = - 2.33
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Interpret results. Since the t-value (-9.8) is less than the t-critical(- 2.33), hence we have to reject the null hypothesis.
b) The observed sample mean produced a t statistic test statistic of - 9.8. Thus the P-value in this analysis is less than 0.0001.
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