A total of n =101 high performance male athletes from eight Canadian sports cent

Question

A total of n =101 high performance male athletes from eight Canadian sports centers were surveyed. The average caloric intake was 3077.0 kcal/day with a standard deviation of 1187.0. The recommended amount is 3421.7. Conduct a hypothesis test to determine whether Canadian high performance male athletes are deficient in their caloric intake.

A). State appropriate null and alternate hypotheses.

B). State the conditions/assumptions under which a test of the claim could be conducted. If the information is not given, please write what you’d have to assume to proceed with the test.

C). Find the test statistic value and the p-value for the hypothesis test.

D). State the conclusion, based on an a=0.05, using statistical terminology.

E). Does your conclusion in d mean the result is statistically significant? Explain, and write your answer in plan language so that someone who knows no statistic could understand.

F). Find a 96% confidence interval for the mean caloric intake of Canadian high performance male athletics.

Explanation / Answer

Back-up Theory

Let X = calorie intake (in kcal/day) per athlete.

Assumption: X ~ N(µ, 2)

‘The recommended amount is 3421.7’ to be interpreted as µ = 3421.7.

2 is not known.

Now, to work out the solution,

Part (A)

Null hypothesis H0 : µ = 3421.7 Vs Alternate hypothesis, HA : µ < 3421.7 ANSWER

[HA is taken as µ <, because the sample average is given to be 3077.0]

Part (B)

The conditions/assumptions under which a test of the claim could be conducted. If the information is not given, please write what you’d have to assume to proceed with the test.

The test can be conducted under the assumption: X ~ N(µ, 2). If this condition is not given, the same test can be conducted by virtue of Central Limit Theorem.

Test differs for ‘2 is not known’ and ‘2 is known’.

In the present case, we will employ the first case. ANSWER

       Part (C)

       The test statistic is t = (n)(Xbar - µ)/s, where n = sample size, Xbar = sample average

and s = sample standard deviation. Substituting the values,

        t = (101)(3077.0 – 3421.7)/1187.0 = - 2.9184 ANSWER 1

        The p-value for the hypothesis test = P(T < - 2.9184), where T ~ t100 [i.e.,

      t-distribution with 100 (101 - 1) degrees of freedom].

       Using Excel Function, p-value for the above statistic = 0.0022 ANSWER 2

Part (D)

Conclusions

Statistically, since the p-value of the test statistic < 0.05, the specified level of significance,

H0 is rejected.

In physical terms, this means that there is enough evidence to suggest that Canadian high performance male athletes are deficient in their caloric intake. ANSWER

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