Independent Random Samples Selected from Two Normal Populations Produced the

question 98

Essay

Independent random samples selected from two normal populations produced the
following sample means and standard deviations. $\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\n_{1}=14 & n_{2}=11 \\\bar{x}_{1}=7.1 & \bar{x}_{2}=8.4 \\s_{1}=2.3 & s_{2}=2.9\end{array}$

Conduct the test $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$ against. $H _ { a } : \left( \mu _ { 1 } - \mu _ { 2 } \right) \neq 0$ , Use $\alpha = .05$ .

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Definitions:

Pearson Correlation

is a measure of the linear correlation between two variables, quantifying the strength and direction of their relationship.

Two-tail Tests

Hypothesis tests that consider extreme values in both tails of the distribution to evaluate the likelihood of observing a relationship by chance in either direction.

Likert Scale

A psychometric scale commonly used in questionnaires to represent people's attitudes, opinions, or perceptions, where responses range from one extreme to another.

Service Quality

The assessment of how well a delivered service conforms to the customer's expectations.