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 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 = 8.6 with sample standard deviation s = 3.5. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 7.4; H1: μ > 7.4 H0: μ = 7.4; H1: μ ≠ 7.4 H0: μ ≠ 7.4; H1: μ = 7.4 H0: μ > 7.4; H1: μ = 7.4 H0: μ = 7.4; H1: μ < 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is unknown. The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is known. The Student's t, since the sample size is large and σ is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood. There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood

Answer 1

Given that, sample size (n) = 41, sample mean = 8.6 and

sample standard deviation (s) = 3.5

a) level of significance = 0.05

The null and alternative hypotheses are,

H0 : μ = 7.4

H1 : μ ≠ 7.4

b) We should use the Student's t, since the sample size is large and σ is unknown.

Test statistic is,

The value of the sample test statistic = t = 2.195

c) Degrees of the = 41 - 1 = 40

Using t-table we get, range for p-value for test statistic = 2.195 at 40 degrees of freedom is, 0.02 < p-value < 0.05

Answer : 0.010 < p-value < 0.050

d) Since, p-value is less than 0.05, we reject the null hypothesis.

Answer : At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

e) Interpretation of conclusion is : There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.