Hypothesis Testing for Teaching Style and Gender

Please see attached file for proper format and formulas.

All work has to be shown. If using SPSS a copy of your output and data file has to be present. Please use formulas.

Below is the data that has to be used to answer all of the questions. The participants were 30 statistics students that were randomly selected to participate in this study. Each question will require use of some portion of this data. It is up to you to use the correct variables and determine the correct analyses.

Statistics Statistics Hours/week
Gender Nationality Pretest Posttest Studied Rank in Class
Male U.S. 15 17 6 6
Female U.S. 14 25 7 28
Male U.S. 10 16 8 7
Female Foreign national 25 30 20 30
Male Foreign national 9 25 30 14
Female U.S. 11 23 15 23
Female U.S. 12 24 12 29
Male U.S. 13 22 15 20
Male Foreign national 13 20 10 15
Male U.S. 15 21 9 19
Female U.S. 17 19 9 9
Female Foreign national 18 20 9 16
Male U.S. 13 24 15 27
Female Foreign national 12 23 14 24
Female U.S. 22 17 11 3
Male Foreign national 17 22 12 21
Female Foreign national 18 24 9 26
Female U.S. 19 20 7 18
Male U.S. 7 17 6 8
Female Foreign national 4 18 5 1
Male Foreign national 13 21 8 17
Female U.S. 15 18 4 10
Female Foreign national 16 18 16 4
Male Foreign national 12 19 19 5
Male U.S. 10 21 12 2
Female U.S. 11 17 9 11
Female Foreign national 18 19 10 12
Female Foreign national 12 22 11 22
Male U.S. 4 24 15 25
Female U.S. 15 26 16 13

Items #1-4.

A researcher wanted to determine whether a new way of teaching statistics was effective. One random sample of 30 students signed up for the statistics class was selected. Each student took the statistics pretest at the beginning of the semester, then experienced the new way of teaching statistics, and took a post-test at the end of the semester. Below are the average pretest
and posttest scores.

Pretest Post-test
___
X = 14 X = 20.17

1. What type of design was used (single sample, independent measures, repeated measures, matched samples)?

2. Write the directional null hypothesis in words.

3. Write the directional null hypothesis in notation.

4. What is the appropriate critical value (?= .05), based on your hypothesis?

Items #5-7.

A researcher wanted to determine whether women outperform men in statistics. Random samples of 17 women and 13 men who signed up for the statistics class were selected. Each student took the statistics posttest at the end of the semester. Below are the average posttest scores.

Women Men
_ _
X = 20.59 X = 19.62
s = 4.27 s = 3.16

The researcher has calculated t and found it to be .68.

5. What type of design was used (single sample, independent measures, repeated measures,
matched samples)?

6. Write the directional null hypothesis in notation. (Make sure it is clear which group is which.

7. Write up these results in APA style.

Items #8-9.

8. In SPSS, construct a scatterplot to show the relationship between the number of hours studied per week and the statistics posttest scores. Comment on the shape of the relationship (linear?) and direction (positive or negative?).

9. In SPSS, using an alpha of .05 and a directional test, conduct a hypothesis test to determine whether there is a relationship between the number of hours studied per week and the statistics posttest scores using all steps of hypothesis testing in order. Be sure to write your hypotheses, find your df and critical value, calculate your test statistic, make your decision regarding the null hypothesis, and write a sentence describing the results in APA style (including all needed
information). Include a copy of your data file.

10. By hand, convert the statistics post-test scores to ranks and conduct a hypothesis test to determine whether there is a relationship between the statistics post-test ranks and student's rank in class scores using all steps of hypothesis testing in order. Be sure to write your hypotheses, find your df and critical value, calculate your test statistic, make your decision regarding the null hypothesis, and write a sentence describing the results in APA style (including all needed
information).

Items #11-12

11. Given the information below, find the regression equation for predicting college grades from vocabulary test scores by hand. Write the equation. Be sure to use the variable names (i.e., posttest scores, pretest scores), not X and Y, in your equation.

College
Grades (X) Vocab.(Y) Grades 2 Vocab 2 Grades x Vocab.
E 605 420 12,629 6408 8600

12. Using the regression equation you found in #9, what would you predict would be the college grade score for a person who has a vocabulary test score = 16?

Items #13-14. The researcher would also like to know whether gender and the nationality of the students are independent of each other. Below is the distribution.

13. By hand, conduct an appropriate analysis to answer this question. Use an alpha of .05. Do the all the steps in hypothesis testing. Be sure to give your hypotheses, your df and critical value, calculate your test statistic, make your decision regarding the null hypothesis, compute the effect size if appropriate, and write a sentence (include all needed information).

Nationality Foreign US
Gender Female 8 9
Male 5 8

14. Explain the statistical assumptions for this test, and determine whether they have been met.

15. If all else remains equal, what happens to the calculated value of t as sample variance increases.

Extra Question: The researcher would like to know whether the current sample of students did significantly better on the statistics posttest than past years' class, who had a mean of u = 20. Using SPSS, conduct the appropriate analysis using an alpha of .05, directional. Do all the steps in hypothesis testing. Be sure to state your hypotheses, state your df and critical value, calculate your test statistic, make your decision, compute effect size if appropriate, and write your sentence (including all needed information).

Extra Question: In SPSS, calculate the 90% confidence interval for the above data, and write a sentence describing the results.