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 = 8.7 with sample standard deviation s = 3.4. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

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

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

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 7.4

H_a : 7.4

Test statistic = t

= ( - ) / s / n

= (8.7 - 7.4) / 3.4 / 41

Test statistic = 2.448

df = 40

P-value = 0.0188

0.010 < P-value < 0.05

= 0.05

P-value <

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

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.