A business journal staff took a sample of 280 companies in 2

A business journal staff took a sample of 280 companies in 2011 and noted that 56 companies among them made acquistions that year. It also selected a sample of 300 companies in 2012 and found that 54 companies among them made acuistions that year. The journal wants to test the current assumption that there is no real difference between the proportion of companies making acquisitions in 2011 and that in 2012, against the alternate possibility that they are different. Use of significance level=0.06

A. State the Null Hypothesis being tested in this case. Also state the Alternate hypothesis.

B. Answer the following questions to defne and calculate the Test Statistic

a. large sample or small sample?

b. Z-statistic or T-statistc

c. give the formula for the test statistic and show the calculation

C. What is the signifcance level a that is to be used?

D. Is this a two-tail, Left-tail or Right-Tail test? Use the distribution tables to find the critical value at this significance level?

E. State and explain your conclusion about the hypothesis in detail. It is not enough to \"Reject Null Hypothesis\" or \"Do Not Reject Null Hypothesis\" Clearly state your reasoning behind the conclusion

Solution

A. State the Null Hypothesis being tested in this case. Also state the Alternate hypothesis.

Let p1 be the proportion in 2011

Let p2 be the proportion in 2012

Null hypothesis: p1=p2

Alternative hypothesis: p1 not equal to p2

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B. Answer the following questions to defne and calculate the Test Statistic

a. large sample or small sample?

Larger sample

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b. Z-statistic or T-statistc

Z test

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c. give the formula for the test statistic and show the calculation

p1=56/280=0.2

p2=54/300=0.18

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.2-0.18)/sqrt(0.2*0.8/280+0.18*(1-0.18)/300)

=0.61

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C. What is the signifcance level a that is to be used?

a=0.06

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D. Is this a two-tail, Left-tail or Right-Tail test? Use the distribution tables to find the critical value at this significance level?

It is a two-tailed test.

Given a=0.06, the critical values are Z(0.06/2) =Z(0.03)=-1.88 or 1.88 (from standard normal table)

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E. State and explain your conclusion about the hypothesis in detail. It is not enough to \"Reject Null Hypothesis\" or \"Do Not Reject Null Hypothesis\" Clearly state your reasoning behind the conclusion

Since Z=0.61 is between -1.88 and 1.88, we do not reject the null hypothesis.

So we can not conclude that they are different