Math  /  Data & Statistics

Question```latex A teacher gave two versions of a quiz, form 1 and form 2, to random samples of sociology students. She wanted to test whether the mean scores would be different if they were given to all sociology students. Here are the raw data.
Form 1 scores: 90, 83, 81, 73, 70, 67, 63, 63, 59, 57, 56, 55, 54, 50, 49, 32, 24, 6.
Form 2 scores: 100, 100, 100, 98, 91, 88, 73, 68, 66, 64, 61, 61, 61, 60, 49, 43, 22.
\begin{enumerate} \item[(a)] Compute the following, rounding to two decimal places. \begin{itemize} \item t=t= \_\_\_\_\_\_\_ \item pp-value == \_\_\_\_\_\_\_ \end{itemize} \item[(b)] Circle the words that make an appropriate conclusion, using α=0.05\alpha=0.05. REJECT / DON'T REJECT the NULL / ALTERNATIVE hypothesis. There IS / IS NOT statistically significant evidence that the mean scores would be THE SAME / DIFFERENT. \end{enumerate}
Skill: Estimate xˉ1xˉ2\bar{x}_{1}-\bar{x}_{2} and the pp-value from a sketch of the sampling distribution.
For each completed sampling distribution for the difference of two means: \begin{enumerate} \item[(a)] Was it a one or two-tailed test? \item[(b)] Write the hypotheses. \item[(c)] What was the SEEsT? \item[(d)] What was the value of xˉ1xˉ2\bar{x}_{1}-\bar{x}_{2}? \item[(e)] Estimate the pp-value (roughly). \item[(f)] Should the null hypothesis be rejected? YES / NO \end{enumerate}
\begin{enumerate} \item[4.] \begin{enumerate} \item[(a)] \_\_\_\_\_\_ \item[(b)] \_\_\_\_\_\_ \item[(c)] \_\_\_\_\_\_ \item[(d)] \_\_\_\_\_\_ \item[(e)] \_\_\_\_\_\_ \item[(f)] YES / NO \end{enumerate} \item[5.] \begin{enumerate} \item[(a)] \_\_\_\_\_\_ \item[(b)] \_\_\_\_\_\_ \item[(c)] \_\_\_\_\_\_ \item[(d)] \_\_\_\_\_\_ \item[(e)] \_\_\_\_\_\_ \item[(f)] YES / NO \end{enumerate} \end{enumerate} ```

Studdy Solution
t2.15t \approx -2.15 p0.04p \approx 0.04 **REJECT** the **NULL** hypothesis.
There **IS** statistically significant evidence that the mean scores would be **DIFFERENT**.
4. (a) Two-tailed (b) H0:μ1=μ2H_0: \mu_1 = \mu_2, Ha:μ1μ2H_a: \mu_1 \ne \mu_2 (c) From StatCrunch output. (d) 15.28\approx -15.28 (e) 0.04\approx 0.04 (f) YES
5. Same as 4.

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