Test Statistic and P-Value

Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly less than 0.86. You use a significance level of α=0.02α=0.02.

      H0:p=0.86H0:p=0.86 

      H1:p<0.86H1:p<0.86

You obtain a sample of size n=354n=354 in which there are 287 successes.

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 four decimal places.) 

p-value = 

The p-value is...

1. less than (or equal to) αα
2. greater than αα

This test statistic leads to a decision to...

1. reject the null
2. accept the null
3. fail to reject the null

As such, the final conclusion is that...

1. There is sufficient evidence to warrant rejection of the claim that the proportion of voters who prefer Candidate A is less than 0.86.
2. There is not sufficient evidence to warrant rejection of the claim that the proportion of voters who prefer Candidate A is less than 0.86.
3. The sample data support the claim that the proportion of voters who prefer Candidate A is less than 0.86.
4. There is not sufficient sample evidence to support the claim that the proportion of voters who prefer Candidate A is less than 0.86.

Answer 1

sample proportion phat = 287/354 = 0.811

test statistic z = (phat - p)/(p*(1-p)/n)^^0.5, where p = 0.86

test statistic z = (0.811 - 0.86)/(0.86 * 0.14/354)**0.5 = -2.657

p-value = P(z < -2.657) = 0.0039

p-value is < alpha

reject null hypothesis

the sample data supports the claim that the proportion of voters who prefer candidate A is less than 0.86.