Question

Since previous studies have reported that elite athletes are often deficient in their nutritional intake (for example, total calories, carbohydrates, protein), a group of researchers decided to evaluate Canadian high-performance athletes. A total of n = 324 athletes from eight Canadian sports centers participated in the study. One reported finding was that the average caloric intake among the n = 201 women was 2403.7 kilocalories per day (kcal/d). The recommended amount is 2811.5 kcal/d.

For one part of the study, n = 114 male athletes from eight Canadian sports centers were surveyed. Their average caloric intake was 3078.0 kilocalories per day (kcal/d) with a standard deviation of 987.0. The recommended amount is 3422.3. Is there evidence that Canadian high-performance male athletes are deficient in their caloric intake?

(c) Construct a 95% confidence interval for the daily average deficiency in caloric intake. (Round your answers to one decimal place.)

= ( , )kcal/day

Note: the answer is NOT (2995,3261)

Answer 1

Since we have to check here that our recommended value 3422.3 is lying in our C.I of interest or not?

using following formula of Confidence interval using test statistic mentioned in below screenshot.

Confidence Interval : [ 2926.4, 3229.6]

Since our recommended value 3422.3 is not lies in obtained C.I. so we may accept H1 here that means there may exist nutritional intake deficiency in male athletes for recommended amount of calorie intake.