A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 141 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) Yes, since $n = 141$ (which is 30 or more).
B) No.
C) Yes, since both $\hat { p } \geq 15$ and $\hat { n q } \geq 15$.
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 141 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) Yes, since $n = 141$ (which is 30 or more).
B) No.
C) Yes, since both $\hat { p } \geq 15$ and $\hat { n q } \geq 15$.
D) It is impossible to say with the given information.

Quizplus · Accepted Answer

The sample size is large enough because both the number of successes ($\hat{p}n$) and failures ($\hat{q}n$) are greater than or equal to 15, which satisfies the conditions for using a normal approximation for the confidence interval.

A Marketing Research Company Is Estimating Which of Two Soft n=141n = 141n=141

A Marketing Research Company Is Estimating Which of Two Soft $n = 141$