Question

In: Statistics and Probability

According to Thomson financials, through January 25,2006, the majority of companies reporting profits had beaten estimates....

According to Thomson financials, through January 25,2006, the majority of companies reporting profits had beaten estimates. Now suppose that for the 4th quarter of 2012, 173 of a random sample of 270 companies reported profits that had beaten estimates.. Use this latest information to answer the following questions.

1) Does the data indicates the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59% at a=0.01?

Please show all 7 steps in detail. step by step.

Solutions

Expert Solution

Step 1:

H0: Null Hypothesis: P 0.59 ( the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59% the proportion of companies in the 4th quarter of 2012 that beat estimates is not greater than 59%)

Step 2:

HA: Alternative Hypothesis: P > 0.59 ( the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59% the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59%) (Claim)

Step 3:

Significance level = = 0.01

Step 4:

n = Sample Size= 270

= Sample Proportion = 173/270 = 0.6407

Step 5:

Test Statistic is given by:

Step 6:

= 0.01

One Tail - Right Side Test

From Table, critical value of Z = 2.33

Rejection Rule:
Reject H0 if Z > 2.33

Step 7:
Since calculated value of Z = 1.695 is less than critical value of Z = 2.33, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59% the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 59%.

orchestra answered 1 year ago
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