Tricky stats question from assignment

[tapciv]

Homework Statement

265 students hire a tutor to help them improve their scores on the SAT test. The results are summarized in Math and Verbal score changes.

Math: Mean change in score = 19, Standard Deviation of score changes = 65
Verbal: Mean change in score = 7, Standard Deviation of score changes = 49.

a) Suppose one of the 265 students is selected at random, give an interval that is likely to contain the students change in the Math Score. I have to do the same for the Verbal as well.

b) Suppose that randomly selected student increased their score on one of the tests by 140 points, which is more likely to be have that increase/why?

Homework Equations

No mean is given, this is where I have become a little stumped. All the questions to date have included a mean (for example the mean score of the 265 students). This question gives me the mean change in score, then the std. deviation of those score changes.

The Attempt at a Solution

I am having trouble making an attempt, not exactly sure where to start.

Any help would be appreciated... thanks!

 

[Bacle2]

Why stumped? You have a statistic --the change in score-- and you know its(sampling) mean and standard deviation, so, using the CLT, given a sample size of 265, you can construct a confidence interval for the change in score.

 

[tapciv]

Thanks for the response. Going over what you said makes sense and I am now going to give it a shot.

Reason I have been stumped with it, we have not been lectured on (I went over my notes, notes in the chapters we are responsible to do, and the power points posted to date) and we have not learned Central Limit Theorem, nor how to construct a confidence interval.

I found the information in the following chapter about CLT and looking for how to construct a confidence interval now...

 

[Bacle2]

If not, let us know what material you have covered.

 

[tapciv]

sure, looking at it it does look like CLT was covering a little in the book but in every example in the book/notes the mean is given (or the direct data points to calculate it). So a question that does not give a mean, rather a mean change in score, I was not sure how to exactly apply the CLT to it.

The confidence intervals have not been covered at all but I think I may have got it.

 

[Bacle2]

But the mean change in score change is just like any other mean in height, weight, prize, etc. You just examine the individual score changes and find the mean of the collection.

 

[tapciv]

Still having some trouble with starting this one out, every question I have done to date has been different, I am not getting how to use the CLT in this case without a mean score given.

Anyone have an example they could lead me to that is similar to this question or perhaps show me how to start this one out? I've been watching some videos and other material but not come across an example quite like this.

Thanks again!