Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:p=0.14Ho:p=0.14
      Ha:p≠0.14Ha:p≠0.14

You obtain a sample of size n=591n=591 in which there are 106 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

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...

in the critical region

not in the critical region

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14.

The sample data support the claim that the population proportion is not equal to 0.14.

There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.14.

Answer 1

Here hypothesis is   vs

Here sample size is 591, out of which there are 106 successful observations, so proportion is

As we see that n is sufficient large and also so we can use normal approximation.

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

Now test statistics is

Here we see that test statistics is in the critical region

As test statistics is in rejection region we reject the null hypothesis

Hence there is sufficient evidence to support the claim that population proportion is not equal to 0.14.

The sample data support the claim that the population proportion is not equal to 0.14.