A recent poll examined the opinions of Americans on the enactment of a law that
ID: 3153150 • Letter: A
Question
A recent poll examined the opinions of Americans on the enactment of a law that would require every gun sold in the U.S. to be test-fired first, so law enforcement would have its fingerprint in case it were ever used in a crime. Independent simple random samples were taken of 510 women and 502 men. When asked whether they would support a ballistic fingerprinting law, 408 of the women, and 370 of the men said "yes." You, as a social scientist would like to explore whether theres is a significant difference in the proportions of women and men who would support this law.
(a) State the research question (or claim).
(b) State the hypotheses.
(c) Calculate the pooled sample proportion.
(d) Calculate the standard deviation (standard error, SE) for the difference between the two proportions.
(e) Determine the critical values.
(f) Calculate the test statistic, and state your decision regarding the null hypothesis.
(g) Calculate the p-value.
(h) Answer the research question, and assess the strength of your conclusion using the p-value. If there is a significant difference, who is more likely to support this law?
(i) Calculate a 95% confidence interval for the difference between the two corresponding population proportions.
(j) How does the result in (i) relate to your conclusion(s) in part (h)?
Explanation / Answer
a) Whether there is significant difference in the proportion of women and men who would support thi slaw.
b) H0: Pu1=Pu2 (equal proportion of women and men will support the law)
H1: Pu1 not equal to Pu2 (there is differnce in proportion of women anad men supporting the law)
c) Pooled sample proportion, Pu is as follows;
Pu=(N1Ps1+N2Ps2)/(N1+N2), where, Ps1, Ps2 refer to sample proportion of men and women and N1 nad N2 refer yto sample sizes of men and women.
Pu= 510*(408/510)+502*(370/502)/(510+502)=0.77
d) SEp-p=sqrt [Pu(1-Pu)] sqrt [(N1+N2)/N1*N2]
=sqrt [0.77(1-0.77) sqrt [(510+502)/510*502]
=0.026
e) Critical values at alpha=0.05 is +-1.96.
f) Z(Obtained)=(Ps1-Ps2)/SEp-p=(408/510-370/502)/0.026=2.42
The test statistic falls in critical region, therefore, reject null hypothesis to conclude that there is differnce in proportion of women and men supporting this law.