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 μ = 7.4.† A newdrug for arthritis has been developed. However, it is thought thatthis drug may change blood pH. A random sample of 36 patients witharthritis took the drug for 3 months. Blood tests showed thatx = 8.6 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: μ = 7.4;H₁: μ > 7.4H₀:μ = 7.4; H₁: μ <7.4    H₀: μ =7.4; H₁: μ ≠7.4H₀: μ ≠ 7.4;H₁: μ = 7.4H₀:μ > 7.4; H₁: μ = 7.4

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

The standard normal, since the sample size is large andσ is unknown.The Student's t, since the samplesize is large and σ is unknown.    TheStudent's t, since the sample size is large and σis known.The standard normal, since the sample size is large andσ is known.

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


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value <0.250    0.050 < P-value <0.1000.010 < P-value < 0.050P-value <0.010

Sketch the sampling distribution and show the area corresponding tothe P-value.

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.At theα = 0.05 level, we reject the null hypothesis and concludethe data are not statisticallysignificant.    At the α = 0.05 level,we fail to reject the null hypothesis and conclude the data arestatistically significant.At the α = 0.05 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.

(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 isinsufficient evidence at the 0.05 level to conclude that the drughas changed the mean pH level of theblood.