A drug to reduce fever was given to a random saple of 8 patients who suffered from high fever. The tempertaure (in celsius) of each patient was measured just before the drug was administered and also measured four hours after the drug was administered. The data is presented in table below. Suppose we want to test at the 1% level of significance whether the drug is effective in lowering fever. Let μ1 denote the mean tempertaure of patients before taking the drug and let μ2 denote the mean temperature of patient four hours after taking the drug . Also let μD=μ1 - μ2. ASSUMING ALL assumption of this test are satisfied Patient 1 2 3 4 5 6 7 8 Before 39.2 38.5 39.7 40.2 38.6 40.4 39.8 39.9 After 40 37.9 39.8 37 38.9 39.1 40.2 37.8 d) what is the observed test statistic for this hypthesis test? e) What is the correct conclusion for this hypthesis test? Since the observed test statistic is greater than the critival value we do not reject H0 at the 1% level of significance Since the observed test statistic is less than critical value we reject H0 at the 1% level of signifcance Since the observed test statistiv is less than the critical value we do not rejectH0 at the 1% level of significance Since the observed test statistic is greater than critical valye we reject H0 at 1% lvel of significance. f) After completing the hypothesis test researchers now decide to estimate μD using a confidence interval. What is the 90% confidence interval for μD?
A drug to reduce fever was given to a random saple of 8 patients who suffered from high fever. The tempertaure (in celsius) of each patient was measured just before the drug was administered and also measured four hours after the drug was administered. The data is presented in table below. Suppose we want to test at the 1% level of significance whether the drug is effective in lowering fever. Let μ1 denote the mean tempertaure of patients before taking the drug and let μ2 denote the mean temperature of patient four hours after taking the drug . Also let μD=μ1 - μ2. ASSUMING ALL assumption of this test are satisfied
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Before | 39.2 | 38.5 | 39.7 | 40.2 | 38.6 | 40.4 | 39.8 | 39.9 |
| After | 40 | 37.9 | 39.8 | 37 | 38.9 | 39.1 | 40.2 | 37.8 |
d) what is the observed test statistic for this hypthesis test?
e) What is the correct conclusion for this hypthesis test?
Since the observed test statistic is greater than the critival value we do not reject H0 at the 1% level of significance
Since the observed test statistic is less than critical value we reject H0 at the 1% level of signifcance
Since the observed test statistiv is less than the critical value we do not rejectH0 at the 1% level of significance
Since the observed test statistic is greater than critical valye we reject H0 at 1% lvel of significance.
f) After completing the hypothesis test researchers now decide to estimate μD using a confidence interval. What is the 90% confidence interval for μD?
Solution:
| Before | After | d = Before - After | ||
| 39.2 | 40 | -0.8 | -1.5 | 2.25 |
| 38.5 | 37.9 | 0.6 | -0.1 | 0.01 |
| 39.7 | 39.8 | -0.1 | -0.8 | 0.64 |
| 40.2 | 37 | 3.2 | 2.5 | 6.25 |
| 38.6 | 38.9 | -0.3 | -1 | 1 |
| 40.4 | 39.1 | 1.3 | 0.6 | 0.36 |
| 39.8 | 40.2 | -0.4 | -1.1 | 1.21 |
| 39.9 | 37.8 | 2.1 | 1.4 | 1.96 |
n= 8 Sample size
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