Letxbe a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of thexdistribution 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 of41patients with arthritis took the drug for 3 months. Blood tests showed thatx=8.4with sample standard deviations=3.1.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:= 7.4;H₁:7.4

H₀:7.4;H₁:= 7.4

H₀:= 7.4;H₁:> 7.4

H₀:> 7.4;H₁:= 7.4

H₀:= 7.4;H₁:< 7.4

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

The Student'st, since the sample size is large andis unknown.

The standard normal, since the sample size is large andis unknown.

The standard normal, since the sample size is large andis known.

The Student'st, since the sample size is large andis known.

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

(c)Estimate theP-value.

P-value > 0.150

0.100 <P-value < 0.150

0.050 <P-value < 0.100

0.020 <P-value < 0.050

P-value < 0.020

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

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.07 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.07 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between2.07 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.07 as well as the area under the curve between 2.07 and 4 are both shaded.

(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?

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

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

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

At the= 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.