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 of31patients with arthritis took the drug for 3 months. Blood tests showed thatx=8.8with sample standard deviations=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?

0.05

(b) 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

(c) What would the sampling distribution be ?

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

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

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

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

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

(e) Estimate theP-value.

P-value > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-value < 0.010

(f )how would the Sketch for the sampling distribution look and show the area corresponding to theP-value.

(g) 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.

(h) 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.