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
Yes, the p-value = 0.287801
No, the p-value = 0.712199
Yes, the p-value = 0.712199
No, the p-value = 0.287801