Question for this hypothesis testing

Question

The government is conducting an unemployment study by taking a random sample with the following results: 350 males and 400 females are chosen. Among those selected, 28 males and 45 females are classified as unemployed.

Based on the given data, is there any sufficient evidence to show that both genders have the same unemployment rates at 20% significance level?

This is a

O lower-tail test

O upper-tail test

O one-tail test

O two-tail test

O none of above

The absolute value of the corresponding critical value needed in this case = ___________ (correct to four decimal places)

The corresponding test statistic in this case = _________ (correct to four decimal places).

Answer 1

This is a two-tailed test (trying to detect if there is any difference).

We are dealing with proportions so we will be using the standard normal probability table. For a level of significance of 0.20, the critical values will corresponding to +/- z score at 90% probability = +/- 1.28

p1 = 28/350 = 0.08 (sample proportion for men)

p2 = 45/400 = 0.1125 (sample proportion for women)

p = (28+45)/(350+400) = 0.097 (pooled sample proportions)

n1 = 350 (sample size men)

n2 = 400 (sample size women)

z = (p1 - p2) / sqrt (p*(1-p)*(1/n1 + 1/n1))

substitute above values and compute

if absolute value of z exceeds 1.28, then the null hypothesis is rejected at level of significance = 0.20