Question

You wish to test the following claim 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=268n=268 in which there are 19 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) αα
   • greater than αα
   
   
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 0.14.
   • There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.14.
   • The sample data support the claim that the population proportion is less than 0.14.
   • There is not sufficient sample evidence to support the claim that the population proportion is less than 0.14.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.14

Ha : p < 0.14

n = 268

x = 19

= x / n = 268 / 19 =0.07

P0 = 0.14

1 - P0 = 1 - 0.14 = 0.86

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.07 -0.14 / [(0.14*0.84) / 268 ]

= -3.299

Test statistic = z = -3.299

P(z < -3.299 ) = 0.0073

P-value = 0.0073

= 0.05

P-value <

0.0073 < 0.05

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.14.