Perform the Indicated Hypothesis Test Use a 010 Significance Level to Test the Claim That the Mean

question 26

Essay

Perform the indicated hypothesis test. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (?1 = ?2), so that the standard error of the difference between means is obtained by pooling the sample variances .
-A researcher was interested in comparing the GPAs of students at two different colleges.
Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. $$\begin{array} { c | c c } \text { College A } & \text { College B } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$$
Use a 0.10 significance level to test the claim that the mean GPA of students at college A is equal to the mean GPA of students at college B. Use the traditional method of hypothesis testing. $$\text { (Note: } \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485 . \text { ) }$$

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Definitions:

Sample Mean

The average of all observations in a sample, calculated by summing the values and dividing by the sample size.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis; it marks the boundary for deciding whether an observed test statistic is extreme.

Null Hypothesis

A statement used in statistical testing that assumes no significant difference or relationship exists between specified populations.

Standard Error

The standard deviation of the sampling distribution of a statistic, commonly used to measure the precision of the sample mean estimate.