Need help with case in statistics

#1
Hi there!

I have just received a case analysis which will in part be basis for my coming exam in statistics. There are no restrictions concerning what sources of information we are allowed to use, including other people (just so you know I'm not cheating).

I will be using SPSS, and I'm especially interested in which statistical methods are the best to analyze the information given in the case. The questions are kinda broad, so the wider the analysis, the better.


Question 1: Kebab

Smp. 1
467 465 519 439 462 482 482 484 465 443 500 430 480 450 460 480 450 470
Smp. 2
524 553

The authorities wanted to control whether the shop had entered costs based on a higher weight per kebab than was the actual case. The first sample consisted of 18 kebabs bought during a single day. The second consisted of two kebabs bought during another day.

a) Combine the samples and analyse the data. Is it reasonable to assume a population mean (average) of 460 gram?

- In this question it seemed reasonable to use a One-Sample t-test comparing means. The results were significant on the 5-percentile.

b) Is it reasonable to assume that the two samples are from the same population? How does this illuminate the authorities’ assessment taxation?

- I'm a litte stuck here. Can Mann-Whitney's test be used when one of the samples contain only 2 observations? Do we have necessary information to run tests?



Question 2: Blonde test

Are blondes more stupid than brunettes? The test consists of five questions, and 46 girls were given the test. We are not told how many of the 46 that were blondes and brunettes. (The scores are in %)

b) Suppose there were 23 girls in each category. Is there a significant difference between blondes and brunettes?

- I found it natural to run a Chi-Square test with a 2X5 matrix. The results weren't significant.

c) Will another distribution of the 46 girls according to blondes and brunettes change the conclusion from b)?

- I'm not quite sure how to test this. I found that changing the distribution changed the results to a certain point, but never enough to be significant.



Question 3: Do stock brokers deserve their commission?

The table (http://home.bi.no/fag87027/met8006/var07/megleranbefalinger.xls) shows the relationship between the number of times a share at Oslo Stock Exchange (OSE) has been recommended during 2006, and the rise in the share’s price during the year. There are a total of 60 shares listed in the tables, half of them with 12 recommendations or more.

a) Analyse the relationship using a fitting model from your curriculum. Let x be the increase in price and y the number of recommendations.

- I used simple regression, and found no correlations whatsoever. Any numbers I should be on the lookout for?

b) The increase in the OSE index was 30,9 % for the period (up to 22/11). Compare this with the increase in price of the shares that were recommended at least 12 times.

- This is the question that bothers me the most, because I have no data on the OSE index besides the mean (and of course the 60 shares which are part of it)! What could they possibly ask for here? Is there a way to compare means using a t-Test with only this information?

That's it, I really hope you guys can help me out and through out as much information as possible.

Here's the case in it's entirety: http://home.bi.no/fag87027/met8006/var07/exc23041_250507case.pdf

Thanks in advance!