Question

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 typically 7.4 (Reference: Merck Manual, a commonly used reference in medical schools and nursing programs). A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 33 patients with arthritis took the drug for 3 months. Blood tests showed that x = 6.9 with sample standard deviation s = 2.7. Use a 10% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H_o: μ  7.4; H₁: μ > 7.4; right-tailedH_o: μ  7.4; H₁: μ < 7.4; left-tailed    H_o: μ < 7.4; H₁: μ > 7.4; right-tailedH_o: μ = 7.4; H₁: μ ≠ 7.4; two-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is unknown.    The standard normal, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known.

(c) Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) State your conclusion in the context of the application.

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

Answer 1