Question

How many calories do you think you burn or expend with 60 minutes of walking on the treadmill? An article that appeared in the American Journal of Men’s Health (2010) presented the results of a study conducted by researchers Harris and George, whose objective was to evaluate how accurately men can estimate their energy expenditure (EE) as measured in kilocalories (kcal). 82 normal-weight and overweight male participants, ages 21–45 years, were recruited from a large, urban university in South Florida. During one session, each participant was made to walk for 60 minutes on a treadmill, and their actual EE was calculated. After they had completed the task, each participant was asked to estimate the number of calories they burned during the task. A summary of the results are shown in the following table.

​	​Sample size	​   Sample average (kcal)	​   Sample SD (kcal)
Difference = ​​Estimated –– Actual	82	x¯d=134	sd=401.37

The researchers wanted to see whether men tended to overestimate or underestimate their EE.

A) On average, did the men in the study significantly overestimate or underestimate their EE? Underestimate/Overestimate/Correct Estimate

B) Explain why a matched pairs test would be appropriate to analyze these data.

Because Each Person has one measurement of their kcal burning and we want to know whether the average difference is different from 0

Because Each Person has one measurement of their kcal burning and we want to know whether the total difference is different from 0

Because Each Person has two measurement of their kcal burning and we want to know whether the average difference is different from 0

Because Each Person has two measurement of their kcal burning and we want to know whether the total difference is different from 0

C) Give the null and alternative hypothesis

The long run average difference in estimated and actual calories burned is not 0. The long run average difference is 0.

The long run average difference in estimated and actual calories burned is 0. The long run average difference is not 0.

The long run average difference in estimated and actual calories burned is 0. The long run average difference is greater than 0.

The long run average difference in estimated and actual calories burned is 0. The long run average difference is less than 0.

D) What assumption do you need to make about the data in order to use the theory-based approach to analyze these data?

Assume the sample size is larger than 20

Assume the population distribution of the differences is not strongly skewed

Assume the sample size is smaller than 20

Assume the population distribution of the differences is strongly skewed

E)  Use the Theory-Based Inference applet to find the standardized statistic and p-value for this test. Round the test statistic to 2 decimal places, e.g. 5.83, and the p-value to 4 decimal places, e.g. 0.0583.

T= _________ P-value____________

F) Use the Theory-Based Inference applet to find a 95% confidence interval. Round your answers to 1 decimal place, e.g. 5.8.
​Confidence interval =_________

G) What conclusions can you draw from the p-value and confidence interval about the strength of evidence?​​​​​​​

Answer 1

A) On average, did the men in the study significantly overestimate or underestimate their EE? Overestimate

B) Explain why a matched pairs test would be appropriate to analyze these data.

Because Each Person has two measurement of their kcal burning and we want to know whether the average difference is different from 0

C) Give the null and alternative hypothesis

The long run average difference in estimated and actual calories burned is 0. The long run average difference is not 0.

D) What assumption do you need to make about the data in order to use the theory-based approach to analyze these data?

Assume the sample size is larger than 20

E)  Use the Theory-Based Inference applet to find the standardized statistic and p-value for this test. Round the test statistic to 2 decimal places, e.g. 5.83, and the p-value to 4 decimal places, e.g. 0.0583.

T= 3.02 P-value = 0.0033

F) Use the Theory-Based Inference applet to find a 95% confidence interval. Round your answers to 1 decimal place, e.g. 5.8.
​Confidence interval = 45.4, 222.6

G) What conclusions can you draw from the p-value and confidence interval about the strength of evidence?

Since the p-value (0.0033) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that men tended to overestimate or underestimate their EE.

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