A Researcher Wants to Determine Whether the Means of Two $\quad$

question 61

Multiple Choice

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table: $\quad$ $\quad$ $\quad$ $\quad$ Sample I $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Sample II
$\begin{array}{llll|lllll}\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \\12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7\end{array}$

She uses the Mann-Whitney U test and a significance level of 0.05.The appropriate
Decision is ______.

• A)reject the null hypothesis that the two populations have different means
• B)fail to reject the null hypothesis that the two populations have different means
• C)reject the null hypothesis that the two populations have equal means
• D)fail to reject the null hypothesis that the two populations have equal means
• E)do nothing

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Definitions:

Variance

A measure of dispersion in a set of data points, calculated by taking the average of the squared differences from the mean.

Standard Deviation

A statistic that quantifies the dispersion or variability of a dataset, measuring the average distance between each data point and the mean.

Z-score

A quantitative measure that demonstrates the correlation of a specific value to the mean of a dataset, identifying its separation from the mean by counting the standard deviations.

Standard Normal Random Variable

A type of random variable that has a mean of 0 and a standard deviation of 1, following the standard normal distribution.