Question

Consider the following hypothesis test Ho: p 2 0.75 a' p < 0.75 A sample of 400 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use α = .05 Round your answers to four decimal places a. p=0.69 p-value Conclusion: p-value less than or equal to 0.05, reject b. p0.72 p-value Conclusion: p-value greater than 0.05, do not reject c. p=0.71 p-value Conclusion: p-value less than or equal to 0.05, reject # d. p=0.78 p-value Conclusion: p-value greater than 0.05, do not reject

Answer 1

a)

For finding p-value first we have to find z score.

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} =\frac{0.69-0.75}{\sqrt{\frac{0.75*(1-0.75)}{400}}} =-2.77$

P-value = P(Z < - 2.77) = 0.0028

b)

For finding p-value first we have to find z score.

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} =\frac{0.72-0.75}{\sqrt{\frac{0.75*(1-0.75)}{400}}} =-1.39$

P-value = P(Z < - 1.39) = 0.0829

c)

For finding p-value first we have to find z score.

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} =\frac{0.71-0.75}{\sqrt{\frac{0.75*(1-0.75)}{400}}} =-1.85$

P-value = P(Z < - 1.85) = 0.0323

d)

For finding p-value first we have to find z score.

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} =\frac{0.78-0.75}{\sqrt{\frac{0.75*(1-0.75)}{400}}} =1.39$

P-value = P(Z > 1.39) = 0.0829