A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children,66 rated it as excellent. Using the 0.1 significance level,the researcher wishes to show that adults like the cereal better than children. What test statistic should we use to compare the ratings of adults and children?
A)A z-statistic
B)A right one-tailed test statistic
C)A left one-tailed test statistic
D)A t-statistic

Question

Quizplus · Accepted Answer

A z-statistic should be used because the sample sizes are relatively large for both the adults (n = 250) and the children (n = 100), and the researcher is comparing two independent groups. Additionally, the question is asking for a one-tailed test (specifically, to test whether adults like the cereal better than children), which means we need to use a z-statistic to find the probability of getting a difference as extreme as the one observed assuming the null hypothesis is true. A t-statistic would be appropriate if the sample sizes were smaller or if the population variances were unknown, but neither of those conditions apply here.

A Sample of 250 Adults Tried the New Multigrain Cereal