Question

5.35 Gaming and distracted eating, Part I: A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate 27.1 grams of biscuits, with a standard deviation of 26.4 grams. Do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is different for the patients in the treatment group? Assume that conditions for inference are satisfied.


What are the hypotheses for this test?

• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} > μ_distraction
• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} < μ_distraction
• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} ≠ μ_distraction

The test statistic for the hypothesis test is:  (please round to two decimal places)
The p-value for the hypothesis test is:  (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:

• Since p < α we do not have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same
• Since p < α we have enough evidence to accept the idea that the average biscuit consumption in the two groups was the same
• Since p < α we have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same, and accept the alternative that distracted eaters will eat a different amount than non-distracted eaters, on average
• Since p < α we have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same, and accept the alternative that distracted eaters will eat more than non-distracted eaters, on average

Answer 1

using excel>addin>phstat>two sample test

we ahve

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	22
Sample Mean	52.1
Sample Standard Deviation	45.1
Population 2 Sample
Sample Size	22
Sample Mean	27.1
Sample Standard Deviation	26.4
Intermediate Calculations
Population 1 Sample Degrees of Freedom	21
Population 2 Sample Degrees of Freedom	21
Total Degrees of Freedom	42
Pooled Variance	1365.4850
Standard Error	11.1416
Difference in Sample Means	25.0000
t Test Statistic	2.2438
Upper-Tail Test
Upper Critical Value	1.6820
p-Value	0.0151
Reject the null hypothesis

Ans ) the hypotheses for this test are

• Ho: μno distraction = μdistraction
  Ha: μno distraction ≠ μdistraction

The test statistic for the hypothesis test is:2.24
The p-value for the hypothesis test is: 0.0151
Interpret the result of the hypothesis test in the context of the study:

• Since p < α we do not have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same