Homework SourseA large pharmaceutical company has recently improved a formu
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
A)
Formulating the null and alternative hypotheses,
Ho: u = 6
Ha: u =/ 6 [ANSWER]
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b)
Here, we use a one sample t test. [ANSWER]
We use it becasue we have a small sample, n = 7.
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c)
We assume the data is approximately normally distributed.
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d)
As we can see, this is a two tailed test.
df = n - 1 = 6
Getting the test statistic, as
X = sample mean = 9
uo = hypothesized mean = 6
n = sample size = 7
s = standard deviation = 2.581988897
Thus, t = (X - uo) * sqrt(n) / s = 3.07408523 [ANSWER, TEST STATISTIC]
Also, the p value is
p = 0.021827595 [ANSWER, P VALUE]
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As P < 0.05, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that this new formula’s duration of cough suppression is different from the old formula’s duration. [CONCLUSION]
