Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,643 ​firms,638 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 α=0.10 to make your decision.

What are the hypotheses for this​ test?

.

H0: p=0.26

Ha: p<0.26

CORRECT ANSWER

What is the rejection​ region? Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to two decimal places as​ needed.).

z < −1.28

Correct answer

Calculate the value of the​ z-statistic for this test.

z=_________-​(Round to two decimal places as​ needed.)

Answer 1

Hypothesis for this test:

H_o: p=0.26

H_a: p<0.26

Left Tailed test:

Given = 0.10;

For Left Tailed Test : Reject null hypothesis if Calculated value of Z is less than Critical Value ;

Rejection region :

Z < - 1.28

n : Sample size: Number of firms in the sample = 2643

p₀: Hypothesized Proportion = 0.26

Number of firms from the sample that announced one or more acquisitions during the year 2000 : x = 638

Sample proportion : = 638/2643 = 0.2414

Test Statistic : z = -2.18