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 = 3.3. 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.

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

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

(c) Estimate the P-value.

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

(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?

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

Answer 1

(a) The level of significance is

The null and alternative hypothesis is ,

(b) Since , the population standard deviation is not known.

Therefore , use t-distribution .

The value of the test statistic is ,

(c) The p-value is ,

p-value= ; The Excel function is , =TDIST(2.328,40,2)

(d) Decision ; here, p-value=0.0251 < 0.05

Therefore , reject Ho.

(e) Conclusion : Hence , there is sufficient evidence to support the claim that the drug has changed the mean pH level of the blood.