In an activity in a statistics class, students were asked if they had ever been
ID: 2909503 • Letter: I
Question
In an activity in a statistics class, students were asked if they had ever been pulled over by a police of?cer while driving. They following table summarizes results, as counts, classi?ed by sex.
(SHOW YOUR WORK)
Ever Pulled Over by Police?
Sex No Yes Total
Male 7 16
Female 20 21
Total
Ever Pulled Over by Police?
Sex No Yes Total
Male
Female
Total
(b) (3 points) Multiply all counts in the table by 10. (The blank table is for you to ?ll in with the new counts) Carry out a chi-square test to determine if there is a relationship between the sex of a student andwhetherheorshehaseverbeenpulledoverbyapoliceof?cerforthepopulationrepresentedbythis sample. (1) Determine the chi-square value rounded to TWO decimal places, degrees of freedom, (2) a range for the p-value and (3) state a conclusion. (Hint: Use the short-cut formula again!)
(c) (2 points) What were the proportions of men and women who had been pulled over by police from the data in the ?rst table and the table multiplied by 10? Compare the results of parts (b) and (c). How has the sample size affected the statistical signi?cance of the observed relationship?
Explanation / Answer
Result:
Sex
No
Yes
Total
Male
7
16
23
Female
20
21
41
Total
27
37
64
(b) (3 points) Multiply all counts in the table by 10. (The blank table is for you to ?ll in with the new counts)
Sex
No
Yes
Total
Male
70
160
230
Female
200
210
410
Total
270
370
640
Carry out a chi-square test to determine if there is a relationship between the sex of a student andwhetherheorshehaseverbeenpulledoverbyapoliceof?cerforthepopulationrepresentedbythis sample. (1) Determine the chi-square value rounded to TWO decimal places, degrees of freedom,
(2) a range for the p-value and (3) state a conclusion. (Hint: Use the short-cut formula again!)
Chi square = 640*(70*210-200*160)^2/ (270*370*230*410) =20.33269
=20.33 ( two decimals)
Degrees of freedom = ( (r-1)*(c-1) = 1
P value < 0.01.
Ho is rejected.
There is a relationship between the sex of a student and whether he or she has ever been pulled over by a police.
(c) (2 points) What were the proportions of men and women who had been pulled over by police from the data in the ?rst table and the table multiplied by 10? Compare the results of parts (b) and (c). How has the sample size affected the statistical signi?cance of the observed relationship?
Proportion for first table:
Male: 16/23=0.6956
Female: 21/41 =0.5122
Proportion for second table:
Male: 160/230=0.6956
Female: 210/410 =0.5122
Proportions were same for the two tables. But second table is significant because of large sample size.
Sex
No
Yes
Total
Male
7
16
23
Female
20
21
41
Total
27
37
64
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