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. 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 x = 8.5 with sample standard deviation s = 2.7. 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.

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.)

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 ?

Interpret your conclusion in the context of the application.

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7 2.9 3.8 4.2 4.8 3.1

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and = 0.78 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.50 grams? Use = 0.05. (a) What is the level of significance?

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

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

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

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 ?

State your conclusion in the context of the application.