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) Both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
B) If $\mathrm { n } 25$, then $\mathrm { n }$ is considered large.
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) Both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$.
B) If $\mathrm { n } > 25$, then $\mathrm { n }$ is considered large.
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

For a sample size to be considered large in the context of proportions, both $\hat { n p } $ (number of successes) and $\hat { n q } $ (number of failures) must be at least 15. This ensures the sampling distribution of the sample proportion is approximately normal, allowing for the use of normal approximation in confidence interval calculations.

A Study Was Conducted to Determine What Proportion of All np^≥15\hat { n p } \geq 15np^​≥15

A Study Was Conducted to Determine What Proportion of All $\hat { n p } \geq 15$