This is Business Statistics problems.

HW 5

1. (35pt) Let π denote the probability that a randomly selected individ- ual supports laws legalizing abortion predicted using gender (G = 0 if gender is male and G = 1 if gender is female), religion affiliation (protestant, catholic or jewish; R1 = 1 if Protestant and 0 otherewise; R2 = 1 if Catholic and 0 otherwise; R1 = R2 = 0 if Jewish) and polit- ical party (democrat, republican or independent ; P1 = 1 if Democrat and 0 otherwise; P2 = 1 if Republican and 0 otherwise; P1 = P2 = 0 if independent). The model used is

logit(π̂) = β0 + β1G + β2R1 + β3R2 + β4P1 + β5P2.

and the estimated logit model is

logit(π̂) = 0.11 + 0.16G− 0.57R1 − 0.66R2 + 0.47P1 − 1.67P2.

(a) (2pt) Estimate the probability that a male, protestant and repub- lican supports laws legalizing abortion. Estimate the probability that female, catholic and democrat supports laws legalizing abor- tion

(b) (2pt) Interpret b1 = 0.16 and b2 = −0.57. (c) (3pt) If SE(b1) = 0.064 construct a 95% confidence interval for

β1 and interpret your result.

(d) (2pt) Test H0 : β1 = 0 against H1 : β1 6= 0 (e) (3pt) If SE(b2) = 0.38 construct a 95% confidence interval for β2

and interpret your result.

2. The Table below appeared in a national study of 15 and 16 year old adolescents. The event of interest is ever having sexual intercourse. The goal is to study the effect if any of race and gender on having sexual intercourse (Yes, No).

Intercourse Race Gender Yes No

White Male 43 134 Female 26 169

Black Male 29 23 Female 22 36

1

Consider the following model

logit(π(Intercourse=Yes|Gender, Race)) = β0 + β1Gender + β2Race

(a) (2pt) Estimate β1 and β2 and interpret your result

(b) (2pt) Estimate the probability of yes for a black female. Estimate the probability of yes for a white male.

(c) (2pt) Construct a 95% confidence interval to describe the effect of gender on the odds of Intercourse controlling for race (i.e. con- struct a 95% interval for eβ1 ), Interpret your result

(d) (2pt) Test H0 : β1 = 0 against Ha : β1 6= 0. Use α = 0.05.

2