Question

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 = 50 male athletes from eight Canadian sport centers were surveyed. The average caloric intake was 3077.0 kilocalories/day with a sample standard deviation of 987.0. The recommended amount is 3421.7. Construct a 95% confidence interval. Please use interval notation and round to two decimal places, (xxxx.xx, xxxx.xx).

Answer 1

Answer:

(3138.29, 3705.11)

Step-by-step explanation:

Given that for sample size of n = 50 male athletes from eight Canadian sport centers  surveyed, the average caloric intake was 3077.0 kilocalories/day with a sample standard deviation of 987.0.

The recommended amount = 3421.70

To construct 95% confidence interval

Since population std deviation is not known we use t critical value for degree of freedom 50-1 =49

t critical = 2.010

Hence margin of error = $2.010*\frac{987}{\sqrt{50-1} } \\=283.41$

Confidence interval lower bound = $3421.70-283.41\\=3138.29$

Confidence interval upper bound = $3421.70+283.41\\=3705.11$

Conf interval = $(3138.29, 3705.11)$