A sample of 12 items yields $\bar { X }$
= 48.5 grams and s = 1.5 grams.Assuming a normal distribution,construct a 90 percent confidence interval for the population mean weight.
A) $\left[ \begin{array} { l l }
47.722 & 49.278
\end{array} \right]$
B) $[ 47.788$$ \quad$$ \quad$$49.212 ]$
C) $\left[ \begin{array} { l l }
45.806 & 51.194
\end{array} \right]$
D) $[ 47.865$$ \quad$$ \quad$$49.135 ]$

Question

A sample of 12 items yields $\bar { X }$
= 48.5 grams and s = 1.5 grams.Assuming a normal distribution,construct a 90 percent confidence interval for the population mean weight.
A) $\left[ \begin{array} { l l } 
47.722 & 49.278
\end{array} \right]$
B) $[ 47.788$$ \quad$$ \quad$$49.212 ]$
C) $\left[ \begin{array} { l l } 
45.806 & 51.194
\end{array} \right]$
D) $[ 47.865$$ \quad$$ \quad$$49.135 ]$

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as $\bar { X }\pm z_{\alpha/2}\frac { s } { \sqrt { n } }$, where $\bar { X }$ is the sample mean, s is the sample standard deviation, n is the sample size, and $z_{\alpha/2}$ is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 90% confidence level, $z_{\alpha/2}$ = 1.645. Plugging in the given values, we get:$48.5 \pm 1.645\frac { 1.5 } { \sqrt { 12 } }$$= 48.5 \pm 1.645\frac { 1.5 } { 3.464}$$= 48.5 \pm 1.645(0.433)$$= 48.5 \pm 0.712$$= [47.788, 49.212]$

A Sample of 12 Items Yields Xˉ\bar { X }Xˉ = 485 Grams and S = 1

A Sample of 12 Items Yields $\bar { X }$ = 485 Grams and S = 1