Construct a 95% Z-Interval or a 95% T-Interval About the Population

question 16

Multiple Choice

Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that
is approximately normal with no outliers.
-The heights of 20 - to 29 -year-old females are known to have a population standard deviation $\sigma = 2.7$ inches. A simple random sample of $n = 15$ females 20 to 29 years old results in the following data:
$\begin{array}{lllll}63.1 & 67.9 & 64.8 & 62.2 & 65.4 \\\hline 63.3 & 66.2 & 68.2 & 69.7 & 64.1 \\\hline 68.4 & 69.9 & 67.3 & 64.5 & 70.2\end{array}$

• A) \(( 64.98,67.72 )\); we are \(95 \%\) confident that the mean height of 20 - to 29 -year-old females is between \(64.98\) and \(67.72\) inches.
• B) \(( 64.85,67.85 )\); we are \(95 \%\) confident that the mean height of 20 - to 29 -year-old females is between \(64.85\) and \(67.85\) inches.
• C) \(( 65.12,67.58 )\); we are \(95 \%\) confident that the mean height of 20 - to 29 -year-old females is between \(65.12\) and \(67.58\) inches.
• D) \(( 65.20,67.50 )\); we are \(95 \%\) confident that the mean height of 20 - to 29 -year-old females is between \(65.20\) and \(67.50\) inches.

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Definitions:

Confidence Interval

An expanse of measurable outcomes, derived from sample analysis, foreseen to incorporate the hidden value of a population attribute.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values from their mean.

Confidence Interval

A range of values, derived from sample data, that is likely to include the value of an unknown population parameter.

Standard Deviation

A statistic that measures the dispersion or variability of a dataset relative to its mean, indicating how spread out the data points are.