Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      Ho:p=0.4Ho:p=0.4
      H1:p>0.4H1:p>0.4

You obtain a sample of size n=327  in which there are 150 successful observations.

The p-value for this test is (assuming HoHo is true) the probability of observing...

• at most 150 successful observations
• at least 150 successful observations

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This p-value 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 greater than 0.4.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.4.
• The sample data support the claim that the population proportion is greater than 0.4.
• There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.4.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.40

Ha : p >  0.40

n = 327

x = 150

= x / n = 150 / 327 =0.46

P0 = 0.40

1 - P0 = 1 - 0.40 =0.60

Test statistic = z

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

=0.46 -0.40 / [0.40*0.60 / 327]

= 2.21

Test statistic = z =2.21

P(z >2.21 ) = 1 - P(z < 2.21 ) = 1 -0.9864

P-value = 0.0136

= 0.02

P-value <

0.0136 < 0.02

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.4