You wish to test the following claim (HaHa) at a significance level of =0.02=0.0

Question

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

      Ho:p=0.75Ho:p=0.75
      Ha:p>0.75Ha:p>0.75

You obtain a sample of size n=726n=726 in which there are 567 successful observations.

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

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

The p-value is...

less than (or equal to)

greater than

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 greater than 0.75.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.75.

The sample data support the claim that the population proportion is greater than 0.75.

There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.75.

Explanation / Answer

p0 = 0.75

p = 567 / 726 = 0.781

a) = sqrt[ p0 * ( 1 - p0 ) / n ] = sqrt(0.75 * 0.25 / 726) = 0.0161

Z = (p - p0) / = (0.781 - 0.75) / 0.0161 = 1.925

b) P-value = P(Z > 1.93)= 1 - P(Z < 1.93) = 1 - 0.9732 = 0.0268

P-value is greater than

c) This test statistic leads to a decision to fail to reject the null

d) There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.75.

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