# Hypothesis testing with two groups and anova

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Answer the questions below, following the Submission Requirements as specified at the end of the assessment. To calculate t when needed, refer to the T-Table for Assessment 4 document linked in the Resources under the Required Resources heading.

Assessment Concepts
Question Topic
Question 1 Standard Error of the Difference Between the Means
Question 2 Standard Error of the Difference Between the Means
Question 3 SPSS: Independent Samples Test
Question 4 SPSS: Independent Samples t Test
Question 5 t Test with Related Samples
Question 6 SPSS: Paired Samples t Test
Question 7 SPSS: Paired Samples t Test
Question 8 Confidence Intervals
Question 9 ANOVA Logic: Partitioning of Deviation Scores
Question 10 ANOVA Logic: From Mean Squares to F
Question 11 ANOVA Summary Table
Question 12 SPSS: One-Way ANOVA
Question 13 SPSS: One-Way ANOVA
Question 14 SPSS: Tukey HSD Test
Question 15 SPSS: Tukey HSD Test

#### Question 1

A researcher examines the results of two separate studies. In the first study, the difference between Group A and Group B is two points. However, the σM1-M2 is large, and the difference is not significant. In the second study, the difference between Group A and Group B is also two points. However, the σM1-M2 is small, and the difference is significant. What might be the reason for the difference in the σM1-M2 across the two studies?

#### Question 2

A researcher is examining the effects of a new anxiety drug. The σM for the experimental group (group receiving the antianxiety drug) is 1.4, while the σM for the control group is 1.22. Calculate the σM1 – M2 .

#### Question 3

Complete the following steps:

1. Open the SPSS file assessment4a.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Analyze, select Compare Means, then select Independent-Samples T Test.
3. Click on Satisfaction Score (the dependent variable), then click on the arrow next to Test Variable(s) to send it over to the Test Variable box.
4. Click on Sample Group (the independent variable), then click on the arrow next to Grouping Variable to send it over to the Grouping Variable box.
5. Click on Define Groups and enter A for Group 1 and B for Group 2. Click Continue.
6. Click OK and copy and paste the output to your Word document.

#### Question 4

A VP for a large clothing retailer is convinced that handing out coupons to customers in the store will leader to higher sales. To test this, she has her sales associates randomly select customers to either receive or not receive a \$10-off, today-only coupon. As each customer leaves the store, the amount of his or her purchase is recorded. The recorded data are in SPSS file assessment4b.sav linked in the Resources under the Required Resources heading.

Complete the following:

1. Identify the IV and DV in this study.
2. State the null hypothesis and the directional (one-tailed) research hypothesis.
3. Run an Independent-Samples T Test using SPSS file assessment4b.sav and paste your output into your Word document. Can you reject the null hypothesis at α = .05? Explain.

#### Question 5

Identify whether independent samples were used, repeated measures were used, or matched samples were used in the following scenarios:

1. A researcher wants to know whether men or women spend more money at the movie concession stand. He asks the concession clerk to identify the customer as male or female on each saved receipt.
2. A CPR instructor wants to know if her students are learning anything during her 90-minute training. She decides to quiz her students at the beginning of class and again at the end of class.

#### Question 6

Complete the following steps:

1. Open the SPSS file assessment4c.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Analyze, select Compare Means, then select Paired-Samples T Test.
3. Click on Preference for Grocery Store A (storea), then click on the arrow to send it over to the Variable 1 box.
4. Click on Preference for Grocery Store B (storeb), then click on the arrow to send it over to the Variable 2 box.
5. Click OK, then copy and paste the output to your Word document.

#### Question 7

A study was conducted on information retention in 40 students (20 pairs) after students conducted online research or watched a movie on a given topic. Students were matched on gender and age. Data provided in the SPSS file below represent quiz scores after students completed their studying.

Complete the following:

1. Open the SPSS file assessment4d.savlinked in the Resources under the Required Resources heading.
2. Conduct a Paired-Samples T Test.
3. Compare t with the one-tailed critical t at the .01 α level. Did the students who studied online score significantly higher on the quiz? Give a decision about the null.

#### Question 8

Refer back to your SPSS output from Assessment 4 Question 3. Based on that output, what is the 95 percent confidence interval of the difference?

#### Question 9

Assume the within-group deviation is 108.45 and the between-group deviation is 48.68. Calculate the total deviation.

#### Question 10

Assume MSbet = 80 and MSwith = 20. What is F?

#### Question 11

Answer questions a–d using the following ANOVA summary table:

ANOVA Summary Table
SS df MS F
Between Groups 283.32 4 70.83 8.16
Within Groups 390.60 45 8.68
Total 673.92 49
1. How many groups participated?
2. How many participants were in each group (assuming equal number of participants per group)?
3. What is the critical value of F (4,45) at the .01 level? Refer to the F-Table for Assessment 4 document linked in the Resources under the Required Resources heading.
4. How confident are you (0–100 percent), given a significant result at the .01 level, that rejecting the null hypothesis is not due to chance? Additionally, what is the probability that you have made a Type 1 error?

#### Question 12

Complete the following steps:

1. Open the SPSS file assessment4e.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Analyze, select Compare Means, then select One-Way ANOVA.
3. Click on Quiz Score (quizscore), then click on the arrow to send it over to the Dependent List box.
4. Click on Student Group (studentgroup), then click on the arrow to send it over to the Factor box.
5. Click OK, and copy and paste the output to your Word document.

#### Question 13

A teacher believes that kindergartners who attend school for a full day are more proficient readers than those children who attend for a half day or those who are homeschooled. At the end of the school year, she gives a reading test to 20 full-day kindergartners, 20 half-day kindergartners, and 20 home-schooled kindergartners. Data provided in the SPSS file assessment4f.sav below represent reading scores for each group:

Complete the following steps:

1. Open the SPSS file assessment4f.sav linked in the Resources under the Required Resources heading.
2. Conduct a One-Way ANOVA in SPSS.
3. State the null hypothesis.
4. Paste the ANOVA table from SPSS into your Word document.
5. Report your results in APA format (as you might see them reported in a journal article).

#### Question 14

Complete the following steps:

1. Open the SPSS file assessment4e.sav.
2. At the top of the screen, click on Analyze, select Compare Means, then select One-Way ANOVA.
3. Click on Quiz Score (quizscore), then click on the arrow to send it over to the Dependent List box.
4. Click on Student Group (studentgroup), then click on the arrow to send it over to the Factor box.
5. Click on Post Hoc, then mark the box next to Tukey. Click Continue.
6. Click OK, and copy and paste the output to your Word document.

#### Question 15

Complete the following steps:

• Open the SPSS file assessment4f.sav.
• Conduct a Tukey HSD at α = .05 in SPSS.
• Copy and paste the output to your Word document.
• Based on your output, identify where the significant differences exist among your kindergartner groups.

#### Submission Requirements

• Submit all answers in one Word document (do not submit multiple files).
• Show your work for questions that require calculations.
• Ensure your answer to each problem is clearly visible (you may want to highlight your answer, or use a different font color, to set it apart).

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