Which Procedures to use for Elementary Statistics on a Data Set

[JamesHawthorne]

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[PaigeMiller]

6. Is the average GPA of the students different for EACH PAIR of 'Year of entry into College."

PROC GLM with the MEANS statement and the T and LINES options.

If any student with High School Class Rank percentile less than 82 is categorized as hrank and lrank otherwise.

- I used proc format to categorize the rank into the two categories of hrank and lrank.

Wouldn't the proportion be 82% for hrank and 18% for lrank (unless there are ties)?

And so I am mystified by the remainder of the questions.

1. Find the 99% confidence interval for the proportion of lrank.

I used the proc freq procedure with tables along with the binomial and alpha options. The proc format made it so that it tests the lrank proportions first (order=formatted). 

2. Is the lrank proportion larger than 50%?

used the proc freq procedure from the previous question and used the p-value to test whether it rejects or fails to reject null hypothesis = .5  

3. Is the proportion of hrank larger then [sic] lrank?

This one I do not know which ones to use. Is it a binomial proportion, chisq test, or something else?

There is no randomness here, so there is no such thing as an hypothesis test. By this I mean, if you take any data, from any distribution, and then if the percentile is less than 82 you call this hrank, you get 82% of your data in hrank, every single time (again, perhaps in the case of ties you get a different result). So the idea of an hypothesis is totally meaningless. Furthermore, the proportion in lrank cannot be larger than 50%, and the proportion in hrank HAS TO BE larger than proportion in lrank.

[JamesHawthorne]

Wouldn't this just be a binomial proportion 1 sample test? Since the HSRANK would have different percentiles of < 82 ranking, and otherwise, per "Year that the student entered high school." Since you're taking random samples each time you test lrank/hrank wouldn't there be some difference in proportion? I am equally as confused with this set of questions.

[PaigeMiller]

Perhaps we are interpreting this differently:

If any student with High School Class Rank percentile less than 82 is categorized as hrank and lrank otherwise.

I don't see how the percent of hrank can be any number other than 82, except in the case of ties.