A company that develops over-the-counter medicines is working on a new product that is meant to shorten the length of sore throats. To test their product for effectiveness, they take a random sample of 110 people and record how long it took for their symptoms to completely disappear. The results are in the table below. The company knows that on average (without medication) it takes a sore throat 6 days or less to heal 42% of the time, 7-9 days 31% of the time, 10-12 days 16% of the time, and 13 days or more 11% of the time.

Can it be concluded at the 0.01 level of significance that the patients who took the medicine healed at a different rate than these percentages? After running a Goodness of Fit test, can it be concluded that there is a statistically significant difference in duration of a sore throat for those that took the medicine and what is the p-value?

6 days or less

7-9 days

10-12 days

13 or more days

Duration of Sore Throat

49

40

12

9

Expected Counts

46.2

34.1

17.6

12.1

Question 4 options:

Yes, the p-value = 0.287801

No, the p-value = 0.712199

Yes, the p-value = 0.712199

No, the p-value = 0.287801