Medicine and Clinical Studies
Young children usually get 5-10 colds each year. To ease cold symptoms, for example, a runny nose or sore throat, some parents give their children over-the-counter cough and cold medicines. However, many of these medicines are not effective and can cause serious side effects in young children. A random sample of parents of young children was obtained and asked whether they give their children cough or cold medicine. The data are given in the following table.
|
Parent
|
Sample Size
|
Number who give cold medicine
|
|
Male
|
376
|
142
|
|
Female
|
428
|
183
|
a. Is there any evidence to suggest that the true population proportion of males who give their children cough medicine is different from the true proportion of females? Use a = 0.05.
b. Find the p value associated with this hypothesis test.
c. Find a 95% confidence interval for the difference in the proportion of males who give their children cold medicine and the proportion of females who give their children cold medicine. Does this confidence interval support your conclusion in part (a)? Why or why not?
d. What must be true of the respondents in order for the hypothesis test in part (a) to be valid?