Question

The test statistic of z=−2.67 is obtained when testing the claim that p= 4 / 7.

a. Using a significance level of α=0.05, find the critical​ value(s).

b. Should we reject Upper H 0H0 or should we fail to reject Upper H 0H0​?

Answer 1

Given , p = 4/7

z = -2.67

a. Using a significance level of α=0.05, find the critical​ value(s).

at α=0.05

z_critical = 1.96

( for two tailed test )

at α=0.05

z_critical = -1.645

( for left tailed test )

b) For two tailed test

reject null hypothesis : |z| > z_critical

|-2.67| > 1.96

or, 2.67 > 1.96

hence, null hypothesis is rejected.

For one tailed test  

reject null hypothesis : z > z_critical

but, -2.67 < -1.645

hence, we fail to reject null hypothesis.