Below are two conventional wisdoms, statements generally believed to be accurate

Question

Below are two conventional wisdoms, statements generally believed to be accurate descriptions of the world. Accompanying each statement are data (from the 2008 General Social Survey) that allow you to test each conventional wisdom. For each statement:

A.   State the null hypothesis.

B.   Calculate the difference between the proportions or means.

C.   Calculate the standard error of the difference in proportions or means.

D.   Using the eyeball test, (i) state whether you would accept the null hypothesis or reject the null hypothesis and (ii) explain your reasoning.

CONVENTIONAL WISDOM ONE: Hispanics have larger families than non-Hispanics. The 2008 General Social Survey asked respondents how many children they have. Hispanic respondents had an average of 1.98 children (standard error = .12), whereas non-Hispanics averaged 1.93 children (standard error = .04).

CONVENTIONAL WISDOM TWO: Southerners are more likely than nonsoutherners to own a gun. According to the 2008 General Social Survey, .43 of southern respondents owned a gun (n = 482), compared with .33 of nonsoutherners (n = 855).

Explanation / Answer

1) let hispanic are 1 and non hispanic are 2

A)null hypothesis:mean1-mean2=0 hispanic and non hispanic have equal family size

alternate hypothesis: mean1>mean2

B)differnce of means x1-x2=1.98-1.93=0.05

C)std error of the difference =(0.122+0.042)1/2=0.1265

d) test stat=(x1-x2)/std error =0.05/0.1265=0.3953.

as test stat z is less then critical value 1.6449 ; we can not reject the null hypothesis.

2)

A)null hypothesis:p1-p2=0

alternate hypothesis: p1>p2

b) difference b/w thw proportions =p1-p2=(0.43-0.33)=0.10

c) std error =(p1(1-p1)/n1)+p2(1-p2)/n2))1/2 =0.0277

d) test stat z=(p1-p2)/std error =3.61

as test stat z is greater then 1.6745 , we reject the null hypothesis.

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