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 \_\_\_\_\_\_\_
\item -value \_\_\_\_\_\_\_
\end{itemize}
\item[(b)] Circle the words that make an appropriate conclusion, using .
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 and the -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 ?
\item[(e)] Estimate the -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
STEP 1
What is this asking?
We're comparing two sets of quiz scores to see if there's a *real* difference in average scores, or if it's just random chance!
Watch out!
Don't mix up the two groups, and make sure we're using the right test in StatCrunch!
Also, let's be super careful with rounding.
STEP 2
1. Calculate Stats for Form 1
2. Calculate Stats for Form 2
3. Perform the t-test
4. Interpret the Results
5. Answer Additional Questions
STEP 3
Let's **add up** all the Form 1 scores: .
Now, **divide** by the number of scores, which is **18**, to get the **mean**: .
STEP 4
Use a calculator or StatCrunch to find the **standard deviation** of Form 1 scores.
We get approximately .
This tells us how spread out the scores are.
STEP 5
Let's **add up** all the Form 2 scores: .
Now, **divide** by the number of scores, which is **17**, to get the **mean**: .
STEP 6
Use a calculator or StatCrunch to find the **standard deviation** of Form 2 scores.
We get approximately .
This shows the spread of these scores.
STEP 7
Input the Form 1 and Form 2 scores into separate columns in StatCrunch.
STEP 8
Go to *Stat* -> *T Stats* -> *Two Sample* -> *With Data*.
Select the columns for Form 1 and Form 2.
Since we're testing for a *difference* (not specifically higher or lower), choose the "not equal" alternative hypothesis.
Click *Compute*.
STEP 9
StatCrunch gives us and .
STEP 10
Our -value () is less than our significance level, .
STEP 11
Since , we **reject** the **null hypothesis**.
This means there's statistically significant evidence that the mean scores on the two forms *are* different!
STEP 12
This was a **two-tailed test** because we were looking for *any* difference, not just one form being higher or lower.
STEP 13
Null Hypothesis : (The means are the same).
Alternative Hypothesis : (The means are different).
STEP 14
The SEEsT is shown in the StatCrunch output.
STEP 15
We found and , so the difference is .
STEP 16
The StatCrunch output gives us the -value directly.
STEP 17
Yes, we reject the null hypothesis.
STEP 18
**REJECT** the **NULL** hypothesis.
There **IS** statistically significant evidence that the mean scores would be **DIFFERENT**.
4. (a) Two-tailed
(b) ,
(c) From StatCrunch output.
(d)
(e)
(f) YES
5. Same as 4.
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