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?

Answer 1

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.