According to Thomson Financial through January 25 2006 the m

According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates. Now suppose that for the 4th quarter of 2012, 222 of a random sample of 300 companies reported profits that had beaten estimates. Use this latest information to answer the following questions.

Does the data suggest the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 69% at ?=0.025?

What is the Null and the Alternative?

What are the critical Values? (+,-, +/-)

Reject the Null if what?

What is the test statistic?

What is the Decision

What is the Conclusion

What is the P-Value

Construct a 98% confidence interval for the true proportion of companies in the 4th quarter of 2012 that beat estimates.

What is the Lower and Upper endpoint?

Solution

What is the Null and the Alternative?

null hypothesis: p=0.69

alternative hypothesis: p>0.69

-----------------------------------------------------------------------------------------------------------

What are the critical Values? (+,-, +/-)

It is a right-tailed test.

Given a=0.025, the critical value is Z(0.025) =1.96 (from standard normal table)

-----------------------------------------------------------------------------------------------------------

Reject the Null if what?

Reject the null if Z>1.96

-----------------------------------------------------------------------------------------------------------

What is the test statistic?

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

=(222/300-0.69)/sqrt(0.69*(1-0.69)/300)

=1.87

-----------------------------------------------------------------------------------------------------------

What is the Decision

Since Z=1.87 is less than 1.96, we do not reject the null hypothesis.

-----------------------------------------------------------------------------------------------------------

What is the Conclusion

So we can not conclude that the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 69%

-----------------------------------------------------------------------------------------------------------

What is the P-Value

The p-value= P(Z>1.87) = 0.0307 (from standard normal table)

-----------------------------------------------------------------------------------------------------------

Construct a 98% confidence interval for the true proportion of companies in the 4th quarter of 2012 that beat estimates.

What is the Lower and Upper endpoint?

phat= 222/300 =0.74

Given a=1-0.98=0.02, Z(0.01)=2.33 (from standard normal table)

So the lower bound is

p -Z*sqrt(p*(1-p)/n) =0.74 - 2.33*sqrt(0.74*(1-0.74)/300) = 0.6809938

So the upper bound is

p +Z*sqrt(p*(1-p)/n) =0.74 + 2.33*sqrt(0.74*(1-0.74)/300) =0.7990062