Question

In 1983, the General Social Survey asked the question, “Do you think a woman should
be able to have an abortion for any reason?” Of the 1515 people asked, 539 said yes; the
rest said no. In 1999, the General Social Survey asked 877 people the same question,
and 361 responded yes; the rest said no. Denote the true proportion of people who felt
that women should be able to have an abortion for any reason in 1983 by p1, and the
proportion in 1999 by p2.
(a) Is there sufficient evidence indicating the proportion of people who felt
that women should be able to have an abortion for any reason increased from 1983
to 1999? Specify the hypothesis, find rejection region at α level and p-value. (Hint:
use pooled sample proportion.)
(b) Argue that the conclusion at α level are equivalent using rejection region and p-value.

Answer 1

The null and alternative hypothesis is as

Ho : There is no sufficient evidence that indicating the proportion of people who felt
that women should be able to have an abortion for any reason increased from 1983
to 1999

H1 : There is sufficient evidence that indicating the proportion of people who felt
that women should be able to have an abortion for any reason increased from 1983
to 1999

Using notation the null and alternative hypothesis is as

Ho : P1 = P2

H1 : P1 < P2

Here P1 & P2 true proportion of 1983 and 1999 respectively

The values provided in the above question are as follows

For computational simplicity we use the notation is as follows

In 1983

X1 = 539

n1 = 1515

In 1999

X2 =361

n2 = 877

1) p1 = sample proportion in 1983

p1 = X1/n1 = 539/1515 = 0.3558

2) p2 = sample proportion in 1999

p2 = X2/n2 = 361/877 = 0.4116

We using the formula of test statistic for used pooled sample proportion is

pooled sample proportion is calculate using following formula

Using all above values in the following formula

Here test statistic Z = -2.7087-----------(1)

Here level of significance α is not given so, we used α = 0.05

Critical value of Z at α = 0.05 = -1.6449---------(2)

We find P value of test statistic using following command in Excel and then press Enter

=NORMSDIST(Z) then press Enter here, =NORMSDIST(-2.7087) = 0.0034

P value = 0.0034

By using P value we decide the null hypothesis is accept or reject by using following condition

1) P value   then we reject Ho

2)  P value   then we accept Ho

In this problem P value = 0.0034 and = 0.05

P value = 0.0034 = 0.05 We reject Ho.

There is sufficient evidence that indicating the proportion of people who felt
that women should be able to have an abortion for any reason increased from 1983
to 1999