Question

Chapter 6, Section 1-HT, Exercise 048

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.

Test H0 : p=0.25vs Ha : p≠0.25 using the sample results p^=0.16 with n=100 Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.

a) test statistic =

b) p-value =

c) Conclusion: (Reject or do not Reject Ho)

Answer 1

a)

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.16 - 0.25) / sqrt ( 0.25 ( 1 - 0.25) / 100 ]

= -2.08

b)

p-value = 2 * P(Z < z)

= 2 * P(Z < -2.08)

= 2 * 0.0188

= 0.038

c)

Since p-value < 0.05 level,

Reject H0