Test Statistics and Critical Value

Question

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:p=0.42Ho:p=0.42 

      Ha:p<0.42Ha:p<0.42

You obtain a sample of size n=139n=139 in which there are 55 successful observations.

What is the critical value for this test? (Report answer accurate to three decimal places.) 

critical value = 

What is the test statistic for this sample? (Report answer accurate to three decimal places.) 

test statistic = 

The test statistic is...

1. in the critical region
2. not in the critical region

This test statistic leads to a decision to...

1. reject the null
2. accept the null
3. fail to reject the null

As such, the final conclusion is that...

1. There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.42.
2. There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.42.
3. The sample data support the claim that the population proportion is less than 0.42.
4. There is not sufficient sample evidence to support the claim that the population proportion is less than 0.42.

Answer 1

Since this is a left-tailed test and the level of significance is 0.02, the critical z value is the z-value for which P(Z < z) = 0.02, which is -2.054.

So reject null hypothesis is sample z statistic < -2.054

The population proportion (p) is 0.42

The sample proportion (phat) = 55/139 = 0.396

The sample size (n) = 139

The sample z-statistic = (phat - p)/(p*(1-p)/n)**0.5

The sample z-statistic = (0.396-0.42)/(0.42*0.58/139)**0.5 = -0.573

The sample z-statistic is not in the critical region, so do not reject null hypothesis.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.42.