5
$\begingroup$

I got this question on a test:

The average jumping distance for males between the ages of 20 to 30 is 6.5 feet with a standard deviation of 0.523 feet. What is the probability, from a sample of 5 males between the ages of 20 to 30, having a sample mean jumping distance between 6 and 7 feet.

I don't want you to solve it for me, but please point out the general workflow for solving such problems, because I don't know where to begin.

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ There are some unstated assumptions here. I'm guessing they want you to compute this using a normal approximation. $\endgroup$
    – cardinal
    Commented Oct 5, 2011 at 18:48
  • $\begingroup$ It's from an Intro to Stats course, so probably the most basic assumptions possible. $\endgroup$
    – twalts
    Commented Oct 5, 2011 at 18:51
  • $\begingroup$ @whuber: What would you say about this rule in faq ? "Don't downvote others who answer homework questions in good faith, even if they break these guidelines. It's not always obvious at first glance that a question is homework, especially when you're not expecting to see it here. It is a good idea to suggest editing the response in a comment." $\endgroup$
    – love-stats
    Commented Oct 5, 2011 at 20:55
  • 1
    $\begingroup$ @love I'm glad you have looked at our FAQ. The question explicitly signals it is homework in the first and last sentences. The record shows that two (discreet and very polite) suggestions were made for you not to display the answer, which you acknowledged but did not act on. In light of this, making more suggestions and waiting for a change in your reply to occur was not a viable option. (It looks like the downvote finally got your attention, though, so it served its purpose.) Consider the deletion of the reply to be a favor to you to prevent any further downvotes. $\endgroup$
    – whuber ♦
    Commented Oct 5, 2011 at 21:09

1 Answer 1

Reset to default
3
$\begingroup$

Questions like this want you to do three things:

  1. Reason from information about the population (mean and SD of jumping distance among males 20 to 30 years old) to the statistical characteristics of a random sample, such as its mean and the standard error of the mean.

  2. Make assumptions that enable you to calculate probabilities based on knowledge of just the mean and standard error of a sample statistic.

  3. Justify those assumptions, to the extent it's possible with limited information.

To do (1) in this instance you are asked about a "mean jumping distance" in a sample. This requires knowledge of the relationships between the (known) mean and SD of the population and the mean and standard error of the sample average. Those relationships, which are simple, depend on the sample size. The purpose of this exercise likely is to give you practice remembering and using these relationships.

Accomplishing (2) depends on the situation. Usually, in introductory courses, problems are chosen so to be solvable using a Normal distribution. Therefore you need to be able to compute probabilities of events like "a normally distributed value is between 6 and 7 feet" based on the mean and SD of that normal distribution. This typically involves re-expressing the limits in terms of standard errors away from the mean and then referring to appropriate tables of the standard Normal distribution. See Normal distribution probability for advice and details. If you know about the Student t distribution you might feel you need to decide whether it would be appropriate here. (Hint: the degrees of freedom depend on how many independent observations were used to estimate the standard deviation of the population. Does the problem tell you this?)

The hard part, emphasized only by good stats courses, concerns justifying the use of a Normal distribution (3) (or whatever distribution you decide to use). Apply your common-sense understanding of people and how their jumping abilities might vary, together with deeper statistical knowledge, such as how representative samples are obtained and what the Central Limit Theorem might suggest. Think about the conditions that could violate those assumptions and what effects they might have on the solution. This element of your response is open-ended (and usually not required in cookbook stats courses), but the more critically and fully you think about it, the deeper your learning will be.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.