A survey conducted recently show the following: of the 200 people interviewed in

Question

A survey conducted recently show the following: of the 200 people interviewed in the US, 160 reported they were jean user. Of another 200 people interviewed in Hong Kong, 140 reported they used jean. The sponsor of the research wanted to know whether the proportion of people who use jeans in the US differs from the proportion of people who use jean in HK? Are there really different (6 points; use 95% confidence level)? Below is the information about 100 respondents to a mail survey concerning smart phone use. Of 100 respondents, 30 are college students (CS) and 70 are not (Non-CS). Please use the information presented in the table below to calculate value the chi^2 value. The number after the slash sign is the expected value for the cell. For instance, the expected value for the first cell is 18. You need to calculate the expected value for Cell 2 and cell 3 first.

Explanation / Answer

(7) here we use z-test of to test of difference of two proportion

with null hypothesis H0:p1=p2 and alternate hypothesis p1 is not equal to p2

here p1=160/200=0.8 and n1=200, var(p1)=p1(1-p1)/n1=0.8*(1-0.8)/200=0.0008

here p2=140/200=0.7 and n1=200, var(p1)=p1(1-p1)/n1=0.7*(1-0.7)/200=0.00105

SE(p1-p2)=sqrt(var(p1)+var(p2))=sqrt(0.0008+0.00105)=0.043

z=(p1-p2)/sqrt(var(p1)+var(p2))=(0.8-0.7)/sqrt(0.0008+0.00105)=2.32

critical z(0.05)=1.96 is less than calculated z=2.32 so we fail to accept H0 and conclude that there is really difference in proportion p1 and p2 with 95% confidence

(8) following information has been generaeted

here chi-square=sum((O-E)2/E)=9.72 with df (r-1)(c-1)=(2-1)*(2-1)=1

Users non-user total C.S. 25 5 30 non-C.S. 35 35 70 total 60 40 100 Expected(E) E Observed(O) (O-E) (O-E)2/E E(25)= 30*60/100= 18 25 7 2.722222 E(5)= 30*40/100= 12 5 -7 4.083333 E(35)= 70*60/100= 42 35 -7 1.166667 E(35)= 70*40/100= 28 35 7 1.75 sum= 100 100 0 9.722222

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