Question

Conduct the following test at the ?=0.05 level of significance by determining (a) the null and the alternative hypothesis, (b) the test statistic, and (c) the critical value. Assuming that the samples were obtained independently using simple random sampling.

Test whether p1?p2. Sample data are x1=28?, n1=255?, x2=36 and n2=302.

(a) Determine the null and alternative hypothesis. Choose the correct answer below.

( ) Ho:p1=p2 versus H1:p1?p2

   ( ) Ho:p1=p2 versus H1:p1>p2

   ( ) Ho:p1=p2 versus H1:p1

(b) The test statistic z0 is ( )    (Round to two decimal places as? needed.)

?(c) The critical values are ± ( ) . (Round to three decimal places as? needed.)

Test the null hypothesis. Choose the correct conclusion below.

   ( ) Reject the null hypothesis.

   ( ) Do not reject the null hypothesis.

Answer 1

We have to test p1 p2

Hypothesis :

Two tailed test.

Test statistics -

Where, is sample proportion of first sample.

= x1/n1 = 28/255 = 0.1098

is sample proportion of 2nd sample.

= x2 / n2 = 36/302 = 0.1192

p is pooled sample proportion.

So test statistics is,

Critical values :

Significance level = = 0.05

Critical values for this two tailed test is -1.96 and 1.96

Decision about null hypothesis :

It is observed that , -1.96 < z₀ = -0.3466 < 1.96

So fail to reject null hypothesis.

Conclusion :

there is not enough evidence to claim that the population proportion p1? is different than p2, at the 0.05 significance level.