Instruction 10-2
a Researcher Randomly Sampled 30 Graduates of an MBA

question 155

Multiple Choice

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.
$\begin{array}{|l|r|}\hline \text { Hypothesised Difference } & 0 \\\hline \text {Level of Significance } & 0.05 \\\hline \text { Population 1 Sample } &\\\hline \text { Sample Size } & 18 \\\hline \text { Sample Mean } & 48266.7 \\\hline \text { Sample Standard Deviation } & 13577.63 \\\hline \text { Population 2 Sample } &\\\hline \text { Sample Size } & 12 \\\hline \text { Sample Mean } & 55000 \\\hline \text { Sample StandardDeviation } & 11741.29 \\\hline \text { Differencein Sample Means } & -6733.3 \\\hline t \text {-Test Statistic } & -1.40193\\\hline \text {Lower-Tail Test } & \\\hline \text {Lower Critical Value }& -1.70113 \\\hline \text {p-Value }& 0.085962\\\hline \end{array}$
-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.From the analysis in Instruction 10-2,the correct test statistic is

• A) -1.4019.
• B) 0.0860.
• C) -6,733.33.
• D) -1.7011.

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Definitions:

Variance

A measure of dispersion showing how much the data points in a set differ from the mean, calculated as the average of the squared differences from the mean.

Final Average

The weighted mean of a student's academic performance across courses over a term or academic year.

Mode

The value that appears most frequently in a data set, representing the most common or popular outcome among the observed values.

Sample Variance

A metric indicating the spread or variation in a set of sample data, determined by dividing the sum of the squared differences from the mean by the total number of data points minus one.