Instead of typing this up I did a search because I knew it had to be somewhere in the literature.
It took a dozen links for me to go with
http://homepage.smc.edu/mcgraw_colle...lc%20Notes.pdf
Read the first two pages.
I would really appreciate help on this. Thankyou
A random survey of 100 students (60 boys/40 girls) asked each student to select the most preferred form of recreational activity from 5 choices. Test whether the choice is independent of the gender of the respondent. Approximate the p-value of the test. Would we reject at ?
Recreational Choice
Basketball (Total=30): Male=21, Female=9
Baseball (Total=8): Male=5, Female=3
Swimming (Total=10): Male=9, Female=1
Running (Total=27): Male=12, Female=15
Tennis (Total=25): Male=13, Female=12
Thankyou!!
Instead of typing this up I did a search because I knew it had to be somewhere in the literature.
It took a dozen links for me to go with
http://homepage.smc.edu/mcgraw_colle...lc%20Notes.pdf
Read the first two pages.
Our null hypothesis is that preference is independent of gender.
If preference is indeed independent of gender, we would expect, for example, men to prefer basektball and women to prefer basketball.
EDIT:
Calculate q.
Q follows a -distribution with (2-1)(5-1) = 4 degrees of freedom (one less than the number of rows times one less than the number of columns)
The p-value for this test is .
This is the smallest significance level at which the null hypothesis can be rejected. So if this value is less than 0.05, then there is enough evidence to reject the null hypothesis.
You can calculate the exact p-value via...
Free p-Value Calculator for the Chi-Square Test
I got q=8.309722222 and with 4 degrees of freedom, the calculator gave me 0.038262. This would mean I could reject the null hypothesis. Is there a formula or chart to find the p-value? I'm curious how that number came about. Thanks
Are you sure you typed in the correct number? For your calculated q I get 0.080870.
According to the following table, the value is somewhere between 0.05 and 0.10.
Table: Chi-Square Probabilities
Thank you for helping! I typed in 8.30972 as the chi square value and 4 degrees of freedom into the calculator provided by matheagle. Thank you for the formula. I have to do a question very similar to this and don't want to get it all wrong. If your answer is correct (which I'm sure it is), then the null hypothesis that gender that preference is independent of gender is NOT rejected?