For hypothesis tests be sure to show all the information req

For hypothesis tests, be sure to show all the information requested: hypotheses, definitions of population parameters used in the hypotheses, the distribution of the test statistic under the null and justification for its use, the test statistic formula and calculation from SAS, pvalue from SAS, the decision (reject or fail to reject H₀) and the final conclusion (stated in the context of the problem).

A large pharmaceutical company has recently improved a formula for cough suppression. The earlier version of the formula relieved cough symptoms for six hours, on average. A trial is held to test whether this new formula’s duration of cough suppression is different from the old formula’s duration. The study recruited seven patients with cough symptoms, and had each patient take the recommended dose of medicine, and the duration of cough symptom relief was measured for each.

That data is reported here, in hours:

11           13           9              7              9              9              5

Using this data, answer the following questions:

a. Specify the null and alternative hypothesis being studied here

b. Which hypothesis test will you use to test the hypotheses you specified above?

c. What assumptions are you making about the data for this test?

d. For the test you specified, calculate the test statistic and p-value

e. Using an of 5%, what do you conclude about the new formula’s effectiveness in relieving cough symptoms?

Solution