5.35 Gaming and distracted eating, Part I: Agroup of researchers are interested in the possible effects ofdistracting stimuli during eating, such as an increase or decreasein the amount of food consumption. To test this hypothesis, theymonitored food intake for a group of 44 patients who wererandomized into two equal groups. The treatment group ate lunchwhile playing solitaire, and the control group ate lunch withoutany added distractions. Patients in the treatment group ate 52.1grams of biscuits, with a standard deviation of 45.1 grams, andpatients in the control group ate 27.1 grams of biscuits, with astandard deviation of 26.4 grams. Do these data provide convincingevidence that the average food intake (measured in amount ofbiscuits consumed) is different for the patients in the treatmentgroup? 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 testis:  (please round to two decimal places)
The p-value for the hypothesis test is:  (pleaseround to four decimal places)
Interpret the result of the hypothesis test in the context of thestudy:

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