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?

(1) State the appropriate H₀.

A)H₀: μ < 3422.3

B)H₀: μ > 3422.3

C)H₀: μ ≤ 3422.3

D)H₀: μ = 3422.3

E)H₀: μ ≠ 3422.3

(2) State the appropriate H_a.

A)H_a: μ > 3422.3

B)H_a: μ ≥ 3422.3

C)H_a: μ = 3422.3

D)H_a: μ ≠ 3422.3

E)H_a: μ < 3422.3

(3)Carry out the test. (Round your answer for t to three decimal places.)

t=

The degree of freedom=

Give the P-value. (Round your answer to four decimal places.) =

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

( , )kcal/day

Answer 1

(1) D)H₀: μ = 3422.3

(2) D)H_a: μ < 3422.3

(3) t=-3.724

degree of freedom=113

p-value=0.0002

t=(x^--μ)/(s/sqrt(n))=(3078-3422.3)/(987/sqrt(114))=-3.724 with n-1=114-1=113 df

p-value=P(t<-3.724)=0.0002

(4)95 % confidence interval (2995,3261)

(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*s/sqrt(n)

95% confidence interval for population mean=3078±t(0.05/2, 113)*987/sqrt(114)=3078±1.98*987/sqrt(114)=3078±183.0=

(2995,3261)