Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-$\mathrm { n } = 30 , \overline { \mathrm { x } } = 90.8 , \mathrm {~s} = 6.2,90 \%$ confidence
A) $88.88

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-$\mathrm { n } = 30 , \overline { \mathrm { x } } = 90.8 , \mathrm {~s} = 6.2,90 \%$ confidence
A) $88.88 < \mu < 92.72$
B) $88.49 < \mu < 93.11$
C) $88.89 < \mu < 92.71$
D) $87.68 < \mu < 93.92$

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as:$ \overline { \mathrm { x } } \pm z ^ { * } \frac { \mathrm { s } } { \sqrt { \mathrm { n } } } $where $ z ^ { * } $ is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 90% confidence level, $ z ^ { * } = 1.645 $. Plugging in the given values, we get:$ 90.8 \pm 1.645 \frac { 6.2 } { \sqrt { 30 } } = 90.8 \pm 1.96 $Therefore, the 90% confidence interval for the population mean is $ ( 88.84 , 92.76 ) $.

Use the Given Degree of Confidence and Sample Data to Construct