Question

You wish to test the following claim at a significance level of α=0.001α=0.001.

Ho:p=0.24Ho:p=0.24
Ha:p<0.24Ha:p<0.24

You obtain a sample of size n=695n=695 in which there are 139 successful observations.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 3 decimal places.
   
2. What is the p-value for this sample?
   
   P-value =  Use Technology Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) α
   • greater than α
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.24.
   • There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.24.
   • The sample data support the claim that the population proportion is less than 0.24.
   • There is not sufficient sample evidence to support the claim that the population proportion is less than 0.24.

Answer 1

Solution:

1)

n = 695

x = 139

Let   be the sample proportion.

= x/n = 139/695 = 0.2

The test statistic z is

z =   

=  (0.2 - 0.24)/[0.24*(1 - 0.24)/695]

= -2.469

test statistic = -2.469

2)

< sign in Ha indicates that the test is "LEFT TAILED "

For left tailed test ,

p value = P(Z < z) = P(Z < -2.469) = 0.0068

P value = 0.0068

3)

The p value is

greater than α

4)

This test statistic leads to a decision to..

fail to reject the null

5)

As such, the final conclusion is that...

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.24.