10. A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6. She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8. Find the critical value to determine whether or not the study guide helped students to increase their test score.
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/probability
related to the Z score. Does that exceed you level of significance?
To determine whether or not the study guide helped students increase their test scores, we can use a two-sample t-test to compare the means of the two groups. The critical value is a value that helps us decide whether the difference in the means is statistically significant.
Here are the steps to calculate the critical value:
1. State the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null hypothesis (H0): The study guide does not have an effect on the test scores.
- Alternative hypothesis (Ha): The study guide helps students increase their test scores.
2. Define the significance level (α):
- The significance level α is a threshold for determining statistical significance. Commonly used values are 0.05 (5%) or 0.01 (1%). Let's assume α = 0.05 for this case.
3. Determine the degrees of freedom:
- The degrees of freedom for a two-sample t-test is calculated using the formula:
Degrees of freedom = (n1 - 1) + (n2 - 1)
Where n1 and n2 are the sample sizes of the two groups.
In this case, we have two groups: the study guide group (n1 = 200) and the non-study guide group (n2 = 200).
Degrees of freedom = (200 - 1) + (200 - 1) = 398
4. Find the critical value:
- The critical value can be obtained from a t-distribution table or calculated using statistical software.
If you have access to a t-distribution table, find the critical value corresponding to the desired significance level (α) and degrees of freedom. Look for a two-tailed test since we are considering both sides of the distribution.
For example, if α = 0.05, and degrees of freedom = 398, the critical value would be approximately ±1.966.
If you prefer to use statistical software, you can input the significance level (α) and the degrees of freedom into the software to obtain the critical value.
Once you have the critical value, you can compare it to the test statistic (calculated from the sample data) to determine whether to reject or fail to reject the null hypothesis.