Question

Chapter 10 and 11 Discussion Group Questions

Scenario 1: A new college student wants to avoid the “freshman 15,” a term used to describe the weight gain common in new college students. He wonders if poultry (chicken) hotdogs really do contain less calories than beef hotdogs. The student collects the calorie counts from several different brands of beef and poultry hotdogs. The student hypothesizes that the calorie count will be lower for poultry hotdogs.

Calories for Poultry Hotdogs (M1)		Calories for Beef Hotdogs (M2)
129		186
132		171
102		176
106		149
94		184
102		190
87		158
99		139
170		175
113		148

1. Define the independent and dependent variable(s).

2. Write a null and alternative hypothesis statement (in words and notation).

3. Is this a directional hypothesis? Yes or No?

4. Should we use a one-tailed or two-tailed test to address our hypothesis? (Hint: use a one-tailed test for directional, and use a two-tailed test for non-directional)

5. Compute the mean, variance (a.k.a. s2), and standard deviation for each type of hotdog.

6. Compute an independent samples t-test to test the hypothesis.

7. What would be the critical value with an alpha of α = .05?

8. Draw a bell curve. Identify the critical value line on the curve. Label the area where we would “fail to reject the null hypothesis”. Label the area where we would “reject the null hypothesis.” Mark where your calculated t is.

9. Do you reject or fail to reject the null hypothesis?

10. What does effect size tell us?

a. Calculate Cohen’s d. What is the size of the effect, according to Cohen’s d?

b. Calculate the r2. What is the size of the effect, according to r2?

11. Write an APA formatted paragraph that explains the results that you found. Here is a help guide to help you with this (pg. 11-12 will be most helpful).Include properly formatted alpha level, test results, significance value (p), and what conclusions you will draw about the hypothesis.

Scenario 2: A computer teacher wants to know if a new training program in keyboarding will improve the students typing speed. The teacher randomly selects ten students to participate in a week of training with the new program. The teacher times their speed before and after the program, to see if the program is worth the time and expense. The teacher hypothesized that the new training program will increase the students typing speed.

Before Course After Course

50 55

42 46

70 78

63 61

58 52

35 45

46 47

52 57

60 71

49 58

1. What is the Research Question? Identify the independent and dependent variables.

2. Write the Null and Alternative Hypothesis (in words and notation) for the research scenario.

3. What is the difference between an independent samples t test and a repeated samples t test?

4. Compute the mean, median, mode, variance, and standard deviation for each data set.

5. Using an alpha level of .01, identify the critical value.

6. Compute a repeated-measures t statistic.

7. Draw out a bell curve and mark the critical region (take care to note if this is a directional hypothesis and label the critical region accordingly). Mark the t-test statistic on the curve as well. Based on the critical value and the t test statistic, what is the conclusion about the null hypothesis (reject or fail to reject)?

8. Compute and interpret the r2.

9. Write an APA formatted paragraph reporting the results. Include properly formatted alpha level, test results, significance value (p), and what conclusion you will draw about the hypothesis.

Answer 1

                                          N   Mean    Variance    StDev
Calories for Poultry Hot        10 113.4     598.711    24.469            
Calories for Beef Hotdog      10 167.6     320.711    17.908     

6. Before compute t value we need to verify whether the population variances are equal or not.

Test and CI for Two Variances: Calories for Pou, Calories for Bee

Method

Null hypothesis         Variance(Calories for Poultry Hotdogs (M) / Variance(Calories for Beef Hotdogs (M2)) = 1
Alternative hypothesis Variance(Calories for Poultry Hotdogs (M) / Variance(Calories for Beef Hotdogs (M2)) not = 1
Significance level      Alpha = 0.05

Statistics

Variable                          N   StDev Variance
Calories for Poultry Hotdogs (M 10 24.469   598.711
Calories for Beef Hotdogs (M2)   10 17.908   320.711

Ratio of standard deviations = 1.366
Ratio of variances = 1.867

Tests

                                                Test
Method                                      DF1 DF2 Statistic P-Value
F Test (normal)                     9    9       1.87      0.366
Levene's Test (any continuous)      1   18       0.08        0.782

Since p-value>0.05 so we can assume population variances are equal. Then

T-Value = -6.07

where Pooled Standard deviation= 21.4409

7. Critical value=-t_0.05,18= - 1.73

8.

9. From the diagram we see that t value falls in rejection region so we reject null hypothesis.