Discuss the below problem:
Q: A medical researcher wants to determine whether there is a difference in the mean length of time it takes three types of pain relievers to provide relief from headache pain. Several headache sufferers are randomly selected and given one of the three medications. Each headache sufferer records the time (in minutes) it takes the medication to begin working. The results are shown in the table. At a significance level of 0.01, can you conclude that the mean times are different? Assume each population of relief times is normally distributed and that the population variances are equal.
|
Medication 1
|
Medication 2
|
Medication 3
|
|
12
|
16
|
14
|
|
15
|
14
|
17
|
|
17
|
21
|
20
|
|
12
|
15
|
15
|
|
19
|
|
|
Mean = 14
|
Mean = 17
|
Mean = 16
|
|
Variance = 6
|
Variance = 8.5
|
Variance = 7
|
a. State the null and alternative hypotheses. Identify the claim
b. Identify alpha.
c. Determine the degrees of freedom.
d. Determine the critical values.
e. Determine the rejection region,.
f. Make a decision to reject or fail to reject the null hypothesis.
g. Interpret the decision in the context of the original claim.