what appropriate null and alternative hypothesis would i use in this problem a teacher gives students a holding review session. did attending the session make a differnts in the final points in the class,give example of the appropriate statisical procedure
Ho: mean1 = mean2
Ha: mean1 ≠ mean2
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
To determine whether attending the review session made a difference in the final points of the class, you can use a hypothesis test. The appropriate null and alternative hypotheses for this problem would be:
Null Hypothesis (H0): Attending the review session does not make a difference in the final points in the class.
Alternative Hypothesis (Ha): Attending the review session does make a difference in the final points in the class.
To find out if there is evidence to reject the null hypothesis and support the alternative hypothesis, you can use a statistical procedure called a hypothesis test for mean difference.
More specifically, you can perform a paired t-test if you have data on the same group of students' final points with and without attending the review session. Paired t-test compares the means of two related groups to determine if there is a significant difference between them.
Here are the steps to perform a paired t-test for this problem:
1. Collect data on the final points of the students who attended the review session and those who did not attend.
2. Calculate the difference in final points (post-session points - pre-session points) for each student who attended the session.
3. Calculate the mean difference in final points for the group.
4. Compute the standard deviation of the differences.
5. Use the t-test formula to calculate the t-value using the sample mean difference, the standard deviation of the differences, the sample size, and the assumed population mean difference (which is zero under null hypothesis).
6. Find the p-value associated with the calculated t-value using a t-distribution table or statistical software.
7. Compare the obtained p-value with the significance level (usually α=0.05) to make a decision regarding the null hypothesis.
If the p-value is less than the significance level, there is evidence to reject the null hypothesis, suggesting that attending the review session has made a significant difference in the final points. If the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis, indicating that attending the review session has not had a significant impact on the final points.
Remember to appropriately interpret the results in the context of the problem and consider any limitations of the study design or data collection process.