Question

For healthy adults, the mean pH of arterial plasma is 7.4 pH. A new drug for arthritis has been developed. However, it is thought this drug might change blood pH. A random sample of 50 patients took this drug for 6 months. Blood tests showed that x =7.1 pH. Assume  = 0.6 pH. Does the sample data indicate that that the drug has changed the mean pH of the blood? Use  = 0.05. 1.

State the null and alternate hypotheses.

What is the level of significance?

2. What is the value of the test statistic?

Answer 1

We have to test whether the drug has changed the mean pH of the blood, here changed means either down or up. So, this is a two tailed hypothesis.

We will use z statistic in this cae because the sample size is large enough to consider it as normal distribution, i.e. sample size is greater than 30

Null hypothesis   (Mean pH is equal to 7.4 or it is unchanged)

Alternate hypothesis (mean pH is changed or it is not equal to 7.4)

Level of significance is 0.05, as it is already mentioned in the question.

Calculation for test statistic z

z =

where

setting the given values, we get

z =

Now, we need to find the corresponding p value

(Using z distribution table)

So, the p value is significant at 0.05 significance level because p value is less than 0.05.

We can reject the null hypothesis and we can conclude that we have enough evidence to support the claim that the mean pH of blood is changed.