Let x be a random variable that represents the pH ofarterial plasma (i.e., acidity of the blood). For healthy adults,the mean of the x distribution is ? = 7.4.† A newdrug for arthritis has been developed. However, it is thought thatthis drug may change blood pH. A random sample of 41 patients witharthritis took the drug for 3 months. Blood tests showed thatx = 8.4 with sample standard deviation s = 3.0.Use a 5% level of significance to test the claim that the drug haschanged (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 therationale for your choice of sampling distribution.

The Student's t, since the sample size is large and? is unknown.

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

The Student's t, since the sample size is large and? is known.

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

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


(c) Estimate the P-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

Sketch the sampling distribution and show the areacorresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will youreject or fail to reject the null hypothesis? Are the datastatistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.

At the ? = 0.05 level, we reject the null hypothesisand conclude the data are not statisticallysignificant.    

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

At the ? = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.

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

There is sufficient evidence at the 0.05 level to conclude thatthe drug has changed the mean pH level of the blood.

There is insufficient evidence at the 0.05 level to concludethat the drug has changed the mean pH level of theblood.