Question

Of 150 adults who tried a new cranberry-flavored peppermint patty, 90 rated it excellent. Of 250 children sampled, 190 rated it excellent. Use the 0.03 level of significance. Regarding whether there is a significant difference in the proportion of adults and the proportion of children who rate the new flavor as excellent, which of the following is correct?

Answer 1

The researcher wanted to test that whether the whether there is a significant difference in the proportion of adults and the proportion of children who rate the new flavor as excellent.

Let p1 be the population proportion of adults.

Let p2 be the population proportion of children.

The null and the alternative hypothesis can be stated as:

The given observed data is:

Sample 1:

Number of adults who tried a new cranberry-flavored peppermint patty (n1) is 150.

Number of adults rated excellent (x1) is 90.

Sample 2:

Number of adults who tried a new cranberry-flavored peppermint patty (n2) is 250.

Number of adults rated excellent (x2) is 190.

The estimated proportion for sample 1 is given by.

The estimated proportion for sample 2 is given by.

Also,

The test statistic is given by,

The p-value obtained from the standard normal table is given by,

Since the p-value (0.00078) is less than the significance level (0.03); the decision is to reject null hypothesis (Ho). In conclusion, there is sufficient evidence to support that there is a statistically significant difference in the proportion of adults and the proportion of children who rate the new flavor as excellent