A group of researchers are interested in the possible effects of distracting sti

Question

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: no distraction = distraction
Ha: no distraction < distraction

Ho: no distraction = distraction
Ha: no distraction > distraction

Ho: no distraction = distraction
Ha: no distraction 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 < we have enough evidence to accept the idea that the average biscuit consumption in the two groups was the same

Since p < 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

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

Since p < 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

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(with pooled variances)

Hypothesis test results:

Hence,

Hypotheses: Ho: no distraction = distraction
Ha: no distraction distraction

Test statistic = 2.24

p - Value = 0.0302

Since p < 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.

Option D is correct

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