Find the Standardized Test Statistic, T, to Test the Claim $\mu _ { 1 } > \mu _ { 2 } .$

question 92

Multiple Choice

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \stackrel { 2 } { 1 } \neq \sigma _ { 2 } ^{ 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \\\overline { \mathrm { x } } 1 = 515 & \overline { \mathrm { x } _ { 2 } } = 500 \\\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25\end{array}$$

• A)1.282
• B)3.271
• C)2.819
• D)1.865

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Definitions:

Level of Significance

A threshold within hypothesis testing used to determine if there is enough evidence to reject the null hypothesis, often set at 0.05.

Critical Value

The threshold value that the test statistic must exceed for the null hypothesis to be rejected, dependent on the chosen significance level.

Alternative Hypothesis

A statement that contradicts the null hypothesis and proposes there is indeed a significant effect or relationship between variables.

Sample Sizes

The number of observations or subjects included in a study from which conclusions are drawn.