Question

11) The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of α found in the one-tail area row. For a left-tailed test, the column header is the value of α found in the one-tail area row, but you must change the sign of the critical value t to −t. For a two-tailed test, the column header is the value of α from the two-tail area row. The critical values are the ±t values shown. Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x 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 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.0 with sample standard deviation s = 1.7. 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 = critical value = ± 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 sufficient 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. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? The conclusions obtained by using both methods are the same. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method. We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 7.4
Alternative Hypothesis, Ha: μ ≠ 7.4

Rejection Region
This is two tailed test, for α = 0.05 and df = 35
Critical value of t are -2.030 and 2.030.
Hence reject H0 if t < -2.03 or t > 2.03

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (8 - 7.4)/(1.7/sqrt(36))
t = 2.118

Reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.

P-value Approach
P-value = 0.0414

The conclusions obtained by using both methods are the same.