Question

The following are the Partial pressure of carbon dioxide (PaCO2 in mmHg) values in 14 patients with bronchopulmonary disease:

38, 41, 45, 48, 49, 56, 60, 75, 42, 48, 32, 33, 33, 36
The data are continuous but do not come from a symmetric population. Use an appropriate test

to test the hypothesis that the PaCO2 values have a population median greater than 40 mmHg. [a] (1 mark) What is an appropriate test for this data set?

[b] Based on your answer in [a], provide the hypotheses of interest using standard notation.

[c] Compute the value of the observed test statistic according to your course notes.

[d] Compute the p-value within table accuracy and provide the distribution used to compute the p-value (including parameter values).

[e] State the strength of evidence against the null hypothesis.

Answer 1

a)

sign test is appropriat here

b)

Ho : median = 40

Ha: median > 40

c)

there are 9 values more than 40, and 5 less than 40

The one-tail P value is 0.2120
This is the chance of observing 9 or more successes in 14 trials.

e) since p-value > alpha

we fail to reject the null hypothesis

we conclude that there is not sufficient evidence that PaCO2 values have a population median greater than 40 mmHg.