Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,905 ?firms, 675 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 26?%? Use ? =0.05 to make your decision. 1) What are the Hypotheses for this test 2) What is the rejection region and 3) Calculate the value of the z-statistic for the test.

Answer 1

1)

H0: p = 0.26

Ha: p < 0.26

2)

Critical value at 0.05 level is -1.645,

Rejection region is reject H0 if test statistics < -1.645

3)

Sample proportion = 675 / 2905 = 0.232

H_0: p = 0.26 H_a: p < 0.26 2) Critical value at 0.05 level is - 1.645, Rejection region is reject H_0 if test statistics < - 1.645 3) Sample proportion p^= 675/2905 = 0.232 Test statistics Z = p^- p/sqrt(p(1 - p)/n) = 0.232 - 0.26/sqrt(0.26 * 0.74/2905) = -3.44 This is test statistics value. Since test statistics < - 1.645, we have sufficient evidence to reject H_0. We conclude at 0.05 level that we have enough evidence to support the claim.

Test statistics

Z = - p / sqrt( p( 1-p) / n)

H_0: p = 0.26 H_a: p < 0.26 2) Critical value at 0.05 level is - 1.645, Rejection region is reject H_0 if test statistics < - 1.645 3) Sample proportion p^= 675/2905 = 0.232 Test statistics Z = p^- p/sqrt(p(1 - p)/n) = 0.232 - 0.26/sqrt(0.26 * 0.74/2905) = -3.44 This is test statistics value. Since test statistics < - 1.645, we have sufficient evidence to reject H_0. We conclude at 0.05 level that we have enough evidence to support the claim.

= 0.232 - 0.26 / sqrt( 0.26 * 0.74 / 2905)

= -3.44

This is test statistics value.

Since test statistics < -1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.