The Student'st distribution table gives critical values for the Student'st distribution. Use an appropriated.f. as the row header. For aright-tailed test, the column header is the value of α found in theone-tail area row. For aleft-tailed test, the column header is the value of α found in theone-tail area row, but you must change the sign of the critical valuet to −t. For atwo-tailed test, the column header is the value of α from thetwo-tail area row. The critical values are the ±t values shown.
Letx be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of thex distribution is μ = 7.4†. A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.0 with sample standard deviations = 1.8. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)
test statistic |
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critical value |
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State your conclusion ion the context of the application.
Reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.Reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level. Fail to reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level.Fail to reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.
Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?
We reject the null hypothesis using the traditional method, but fail to reject using theP-value method.The conclusions obtained by using both methods are the same. We reject the null hypothesis using theP-value method, but fail to reject using the traditional method.