5.35 Gaming and distracted eating, Part I: A group of researchers are interested

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 greater for the patients in the treatment (solitaire, distracted) group? Assume that conditions for inference are satisfied. Use a 5% significance level. USE YOUR TI CALCULATOR.


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

5.7 Sleep habits of New Yorkers: New York is known as "the city that never sleeps". A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. Do these data provide strong evidence that New Yorkers sleep less than 8 hours a night on average? Use a significance level of 5%. USE YOUR TI CALCULATOR.

(a) Write the hypotheses in symbols.

Ho: = 8
Ha: > 8

Ho: = 8
Ha: 8

Ho: = 8
Ha: < 8

(b) Calculate the test statistic, T, and the degrees of freedom.
T = (please round to two decimal places)
There are  degrees of freedom associated with this test.


(c) Find the p-value in this context.
p =  (please round to four decimal places)


(d) What is the conclusion of the hypothesis test?

Since p we reject the null hypothesis and accept the alternative. These data provide evidence that New Yorkers sleep less than 8 hours a night on average

Since p< we reject the null hypothesis and accept the alternative. These data provide evidence that New Yorkers sleep less than 8 hours a night on average

Since p< we fail to reject the null hypothesis. These data do not provide evidence that New Yorkers sleep less than 8 hours a night on average

Since p we accept the null hypothesis. These data provide evidence that New Yorkers sleep less than 8 hours a night on average

Since p we do not have enough evidence to reject the null hypothesis. These data provide evidence that New Yorkers sleep less than 8 hours a night on average

(e) If you were to construct a 90% confidence interval that corresponded to this hypothesis test, would you expect 8 hours to be in the interval?

no

yes

Explanation / Answer

a)

Ho: = 8
Ha: < 8

b) std error of mean =std deviation/(n)1/2 =0.57/(25)1/2 =0.114

tehrefore test statistic t=(X-mean)/std error =(7.73-8)/0.114=-2.37

c) p value =0.0131

d)

Since p< we reject the null hypothesis and accept the alternative. These data provide evidence that New Yorkers sleep less than 8 hours a night on average

e)

no

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

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