A new drug designed to reduce fever is being tested for efficacy and side effects. Ten patients entering a hospital with a high fever were selected at random. The temperature (in ◦F) of each patient was measured, the drug was administered, and two hours later,the temperature was measured again. The data are provided in the table below. Patient Before Drug After Drug Difference (Before - After) 1 102.6 99.8 2.8 2 99.2 98.8 0.4 3 102.3 97.5 4.8 4 101.1 100.3 0.8 5 102.7 99.6 3.1 6 102.6 102.8 -0.2 7 100.5 99.0 1.5 8 103.5 101.8 1.7 9 105.7 97.1 8.6 10 104.3 99.2 5.1 Mean 102.44 99.59 2.85 Standard Deviation 1.867 1.746 2.680 (a) Conduct the appropriate hypothesis test to determine whether there is any evidence that the new drug reduces the mean patient temperature after two hours. Use α =0.05. For hypothesis testing, do not use p-values to reach a Decision/Conclusion. Instead, Define the parameter(s) of interest, State the Hypotheses, Test statistics, T observed, Rejection Region, and mention the significance level used in the hypothesis test either in the Decision or in the Conclusion. (b) What assumption(s) must be satisfied for your test to be valid?
A new drug designed to reduce fever is being tested for efficacy and side effects. Ten patients entering a hospital with a high fever were selected at random. The temperature (in ◦F) of each patient was measured, the drug was administered, and two hours later,the temperature was measured again. The data are provided in the table below.
Patient Before Drug After Drug Difference (Before - After)
1 102.6 99.8 2.8
2 99.2 98.8 0.4
3 102.3 97.5 4.8
4 101.1 100.3 0.8
5 102.7 99.6 3.1
6 102.6 102.8 -0.2
7 100.5 99.0 1.5
8 103.5 101.8 1.7
9 105.7 97.1 8.6
10 104.3 99.2 5.1
Standard Deviation 1.867 1.746 2.680
(a) Conduct the appropriate hypothesis test to determine whether there is any evidence that the new drug reduces the mean patient temperature after two hours. Use α =0.05. For hypothesis testing, do not use p-values to reach a Decision/Conclusion. Instead, Define the parameter(s) of interest, State the Hypotheses, Test statistics, T observed, Rejection Region, and mention the significance level used in the hypothesis test either in the Decision or in the Conclusion.
(b) What assumption(s) must be satisfied for your test to be valid?
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