Dr. Johnson, a renowned dietician, has consistently proclaimed the benefits of a

Question

Dr. Johnson, a renowned dietician, has consistently proclaimed the benefits of a balanced breakfast. To substantiate her claim, she asks participants to go without breakfast for one week. The following week she asks the same participants to make sure they eat a complete breakfast. Following each week, Dr. Johnson asks each participant to rate their productivity for that week. Show your computational work and write your final answers for each of the questions below. No work or unclear work = No credit

Participant

Performance with Breakfast

Performance without Breakfast

#1

8

6

#2

6

6

#3

8

5

#4

8

5

What are the two-tailed null and research hypotheses in the example above? (4 points)

What are the mean scores for each of the two groups? (2 points)

What is the standard deviation for the participants’ ratings? (4 points) What is the standard error of the mean difference for the participants’ ratings? (4 points)

What kind of t-test should you use in this case, and why? [e.g. independent groups (w/ or w/o equal variances), same sample measured twice, matched samples, test of differences between proportions, etc. 2 points]

Using = .05, do a two-tailed test of the doctor’s hypothesis (4 points). Be sure to include how you calculated the df and critical value (2 points), as well as your conclusions about the test results (2 points).

Participant

Performance with Breakfast

Performance without Breakfast

#1

8

6

#2

6

6

#3

8

5

#4

8

5

Explanation / Answer

1. The Mean score of each group is

Descriptive Statistics: with breakfast, without breakfase

Variable Count Mean StDev Variance
with breakfast 4 7.500 1.000 1.000
without breakfase 4 5.500 0.577 0.333

2. The  standard deviation for the participants’ ratings is

Descriptive Statistics: difference

Variable Count Mean StDev Variance
difference 4 2.000 1.414 2.000

Standard errir: 1.414 / sqrt(4) = 0.707

3. we have to use matched samples - t test (paired sample t test)

4. Test statistic = (7.5-5.5) / 0.707 = 2.8288

5. t - critical value: 3.18245

Here t value < t critical value so we accept H0

thus we conclude that there is no significance difference between the means of two groups

with breakfast without breakfase difference 8 6 2 6 6 0 8 5 3 8 5 3

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.