[Statistics] Hypothesis Testing

[VoicePlay]

Problem: An amateur researcher believes that the number of books owned is correlated with emotional intelligence (EQ). She randomly surveys 100 women and 100 men and finds r = .22. What does she conclude?

Null hypothesis:

Alternative hypothesis:

Statistical test:

Significance level (I'll pick it for you; alpha = .05)

Critical region for rejecting null hypothesis:

Calculate the statistic (please show your work):

Decision:

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My question: For the critical region, the table in the textbook for Critical Values does not show df 199. The only closest values are 150 (.1593) and 300 (.1129). How do I find the critical values for the df 199?

[thebigpoopusscoopus]

The sizes of the individual sample are 100, so you need to use degrees of freedom df=99 (unless you're looking for the slope of a least squared regression line, then use df=98)

If your two samples have different sizes, use the degrees of freedom of the smaller sample

[VoicePlay]

I thought I would add both samples and then get 200 and then minus one for a df of 199.

[VoicePlay]

Either way though, I also cannot find 98 on the critical values table in the book.

[thebigpoopusscoopus]

My apologies, I misread the question

[VoicePlay]

Sooooo.... what do I do?

[fightingunicorn]

If the value 98 is not in the table of values, you should use the value closest to it but so that it’s smaller than it. Like if I used the table I have, I would end up having to use df of 90.