Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,995 ​firms, 741 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 27​%? Use α=0.01 to make your decision.

What are the hypotheses for this​ test?

A. H0​: p > 0.27

Ha​: p ≤ 0.27

B. H0​: p < 0.27

Ha​: p = 0.27

C. H0​: p ≠ 0.27

Ha​: p = 0.27

D. H0​: p=0.27

Ha​: p > 0.27

E. H0​: p = 0.27

Ha​: p ≠ 0.27

F. H0: p = 0.27

Ha: p < 0.27

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.)

A. z < ______

B. z > ________

C. z < _______ or z > ______

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

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

What is the conclusion of the​ test?

(Reject, Do not reject) the null hypothesis because the test statistic( is,is not),in the rejection region.​ Therefore, there is( sufficient, insufficient) evidence at the 0.01 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 27​%.

Answer 1

To test against

At 1% level of significance,

The rejection region is :

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

Now,

The value of the test statistic

and critical value

Since , we reject H₀ at 1% level of significance and we can conclude that :

there is sufficient evidence at the 0.01 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 27​%..