Question

In a random sample of 200 adults, 136 say they are in favor of outlawing cigarettes in certain areas. Let p  be the proportion of all adults who are in favor of outlawing cigarettes. One is interested for the following hypotheses:  H 0: p = 0.6   vs H a: p > 0.6.

Find the rejection region with significance level .05.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.6

Ha : p > 0.6

= x / n = 136/200=0.68

P0 = 0.6

1 - P0 = 0.4

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.68-0.6/ [(0.6*0.4) /200 ]

= 2.31

P(z >2.31 ) = 1 - P(z < 2.31) = 1-0.9896=0.0104

P-value = 0.0104

= 0.05

P-value >

fail to Reject the null hypothesis .