Question

10
a professor wanted to determine what percent of college students are also working (either full time or part - time). the professor randomly selects 400 college students
and finds that 23% of them are working. identify the correct formula and/or calculator function that would be used to construct a confidence interval for the proportion of
college students who are also working.
formula: \\( \hat { p } \pm z _ { \frac { a } { 2 } } \sqrt { \frac { \hat { p } ( 1 - \hat { p } ) } { n } } \\)
calculator function: 1 - propzint
formula: \\( l b = \sqrt { \frac { ( n - 1 ) s ^ { 2 } } { x ^ { 2 } _ { \frac { a } { 2 } } } } \\)
and
\\( u b = \sqrt { \frac { ( n - 1 ) s ^ { 2 } } { x ^ { 2 } _ { 1 - \frac { a } { 2 } } } } \\)
formula:
\\( l b = \frac { ( n - 1 ) s ^ { 2 } } { x ^ { 2 } _ { \frac { a } { 2 } } } \\)
and
\\( u b = \frac { ( n - 1 ) s ^ { 2 } } { x ^ { 2 } _ { 1 - \frac { a } { 2 } } } \\)
formula: \\( \overline { x } \pm t _ { \frac { a } { 2 } } \cdot \frac { s } { \sqrt { n } } \\)
calculator function: t - interval

Explanation:

Step1: Identify the problem type

We are dealing with a confidence interval for a proportion. The formula for a confidence interval for a proportion is $\hat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, and the calculator function for a one - proportion confidence interval is 1 - PropZInt.

Step2: Analyze other options

• The formulas involving $s^{2}$ (sample variance) and $\chi^{2}$ (chi - square) are for confidence intervals of variances.
• The formula $\bar{x}\pm t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}$ is for confidence intervals of means (when the population standard deviation is unknown).

Answer:

Formula: $\hat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, Calculator Function: 1 - PropZInt (the first option)