Question

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 μ = 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 41 patients with arthritis took the drug for 3 months. Blood tests showed that x-bar = 8.5 with sample standard deviation s = 2.9. 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 α? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

αα =

H0H0: μμ =

H1H1: μμ Select an answer not = < >  

The test is a Select an answer two-tailed left-tailed right-tailed  test

b.) Identify the Sampling Distribution you will use. What is the value of the test statistic?

The best sampling distribution to use is the Select an answer Normal Student's t  distribution.

The test statistic (z or t value) is =

c.) Find or estimate the P-value for the test.

The p-value is = Select an answer Between 0.050 and 0.075 Between 0.025 and 0.050 Between 0.100 and 0.125 Between 0.010 and 0.025 Between 0.075 and 0.100

d.) Conclude the test.

Based on this we will Select an answer Reject Fail to reject  the null hypothesis.

Answer 1

Solution:

a)

α = 5% = 0.05

H0: μ = 7.4

H1: μ 7.4

The test is a two-tailed.

b)

The best sampling distribution to use is Student's t  distribution.

(Because the population standard deviation is unknown)

Test statistic t is

t =

= (8.5 - 7.4/(2.9/41)

= 2.429

The test statistic (t value) is = 2.429

c)

df = n - 1 = 41 - 1 = 40

Two tailed test

t = 2.429

SO , using t table ,

The p-value is Between 0.010 and 0.025

d)

Reject the null hypothesis.

(because p value is less than 0.05 level)