A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 148 college students produced the following confidence interval for the
Proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for
This analysis to work?
A) No.
B) Yes, since both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
C) Yes, since $n = 148$ (which is 30 or more).
D) It is impossible to say with the given information.

Question

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 148 college students produced the following confidence interval for the
Proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for
This analysis to work? 
A) No.
B) Yes, since both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
C) Yes, since $n = 148$ (which is 30 or more).
D) It is impossible to say with the given information.

Quizplus · Accepted Answer

The sample size is large enough for the analysis because both conditions $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$ are likely met. The confidence interval for the proportion suggests that the sample proportion ($\hat{p}$) is within the interval (.344, .494), and with a sample size of 148, the estimated number of successes ($\hat { n p }$) and failures ($\hat { n q }$) can be calculated and are likely to both exceed 15, satisfying the rule of thumb for the minimum expected successes and failures for the normal approximation to be appropriate.

A Marketing Research Company Is Estimating Which of Two Soft np^≥15\hat { n p } \geq 15np^​≥15

A Marketing Research Company Is Estimating Which of Two Soft $\hat { n p } \geq 15$