A5 P5

A5 P5#

Researchers want to investigate if the daily caloric intake of elite male athletes is less than the recommended daily intake of \({{ params.mu }}\) kcal/d. Suppose a sample of \(n = {{ params.size }}\) elite male athletes were reported to have an average caloric intake of \({{ params.X_bar }}\) kcal/d. Assume \(\sigma = {{ params.sigma }}\) and \(\alpha = {{ params.alpha }}\) when answering the following.

Round all numbers to three decimal places.

Part 1#

Create a \({{ params.percent}}\)% confidence interval for \(\mu\). Provide the lower and upper bound in the matrix in the format [lower, upper].

Answer Section#

Part 2#

How wide is the confidence interval from the previous question?

Answer Section#

Part 3#

What is the null hypothesis?

Answer Section#

  • \(H_0: \mu = 3919.2\)

  • \(H_0: \mu = 3432.4\)

  • \(H_0: \bar{x} = 3432.4\)

  • \(H_A: \mu = 3919.2\)

  • \(H_0: \mu \lt 3919.2\)

Part 4#

What is the alternative hypothesis?

Answer Section#

  • \(H_A: \mu \neq 3919.2\)

  • \(H_A: \mu \lt 3919.2\)

  • \(H_A: \mu \le 3919.2\)

  • \(H_0: \mu \lt 3919.2\)

  • \(H_A: \bar{x} \lt 3919.2\)

Part 5#

What is the critical value?

Answer Section#

  • \(1.282\)

  • \(1.645\)

  • \(1.96\)

  • \(2.326\)

  • \(-1.282\)

  • \(-1.645\)

  • \(-1.96\)

  • \(-2.326\)

Part 6#

What distribution does the test statistic \(Z\_{obs}\) follow? Please note that we are parameterizing the Normal distribution using the standard deviation, i.e. of the form \(\operatorname{N}(\mu,\sigma)\).

Answer Section#

  • \(\operatorname{N}(0,1)\) (Standard Normal)

  • \(\operatorname{N}(3919.2, 986)\)

  • \(\operatorname{N}(3919.2, 986/\sqrt{14})\)

  • \(t_{n-1}\)

  • \(t_n\)

Part 7#

What is the value of the observed test statistic?

Answer Section#

Part 8#

What is the \(p\)-value as approximated by the \(Z\)-table? To match the \(Z\)-table, keep you answer with 4 decimal places.

Answer Section#

Part 9#

What is the exact \(p\)-value as computed in R? (Do not round your answer)

Answer Section#

Part 10#

Based on this sample, what would be our generic conclusion (select the most correct)

Answer Section#

  • Reject the null hypothesis

  • Reject the null hypothesis in favor of the alternative hypothesis

  • Fail to reject the null hypothesis

  • Accept the alternative hypothesis

  • Accept the null hypothesis

Part 11#

Based on this sample, how might we phrase our non-generic conclusion (select the most appropriate answer)?

Answer Section#

  • There is sufficient evidence to suggest that the average caloric intake of elite male athletes is less than 3919.2 kcal/d.

  • There is sufficient evidence to suggest that the average caloric intake of elite male athletes is different than 3919.2 kcal/d.

  • There is insufficient evidence to suggest that the average caloric intake of elite male athletes is less than 3919.2 kcal/d.

  • There is sufficient evidence to prove that the average caloric intake of elite male athletes is less than 3919.2 kcal/d.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.