A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814,
0.75186). The sample size that was used in this problem is considered a large sample. What criteria should be used to determine if n is large?
A) If $\mathrm { n } 25$, then $\mathrm { n }$ is considered large.
B) Both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
C) When working with proportions, any $\mathrm { n }$ is considered large.
D) If $\mathrm { n } \geq 30$, then $\mathrm { n }$ is considered large.

Question

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814,
0.75186). The sample size that was used in this problem is considered a large sample. What criteria should be used to determine if n is large? 
A) If $\mathrm { n } > 25$, then $\mathrm { n }$ is considered large.
B) Both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
C) When working with proportions, any $\mathrm { n }$ is considered large.
D) If $\mathrm { n } \geq 30$, then $\mathrm { n }$ is considered large.

Quizplus · Accepted Answer

The criteria for a large sample size in the context of proportions is that both $\hat{n}p \geq 15$ and $\hat{n}q \geq 15$, where $\hat{p}$ is the sample proportion and $\hat{q} = 1 - \hat{p}$.

A Study Was Conducted to Determine What Proportion of All n>25\mathrm { n } > 25n>25

A Study Was Conducted to Determine What Proportion of All $\mathrm { n } > 25$