Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 ,767 ​firms, 705 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=0.10 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​: ≤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<_________ orz>_________

B. z<___________

C.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

▼

insufficient

sufficient

evidence at the 0.10

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

The Hypotheses are:

Ho: P=0.27

Ha: P<0.27

Rejection region :

Reject Ho if Z_obs<Z_0.10=-1.282

Test statistic:

The test statistic is calculated by

P value :

P value associated with Z score is calculated using the Z score table or by excel tool as

P-value=0.03593

Conclusion:

Since Z_obs=1.802<Z_0.10=-1.282 and P- value is <0.01 (Level of significance) hence we reject the null hypothesis and conclude that it has enough evidence to support the claim.

The table as: