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 = 7.4 (Reference: The 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 31 patients with arthritis took the drug for 3 months. Blood tests showed that = 8.1 with a sample standard deviation = 1.9. 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 alternative hypotheses. b) What sampling distribution will you use? How many degrees of freedom will we use (if appropriate)? Explain the rationale for your choice of sampling distribution. c) Compute the appropriate sampling distribution of the sample test statistic. d) Find the critical value. e) Based on your answers in parts (a) through (d), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? f) Interpret your conclusion in the context of the application