Question

assume that the significance level is a =0.1. use the given information to find the p value and the critical values. the test statsitc of z= -0.75 is obtained when testing the claim that p < 0.1

a. what is the p value

b. what are the critical values

Answer 1

Here the test is,

H₀: p = 0.1 vs H₁: p < 0.1

a) Here the p-value of the test is P[Z < z] where Z follows N(0,1) and z is the observed value of the test statistic.

So, here it is P[Z < -0.75] = 0.2266274.

Here the p-value > 0.1, so we can't reject the null hypothesis.

b) Here the critical value of the test is the lower 1/10^th value of N(0,1).

So, the critical value is  -1.281552.

Here the test statistic is greater than the critical value so we can't accept the null.

Note: Here we can have one critical value as the test is left tailed test.