According to Thomson Financial, through January 25, 2006, the majority of compan

Question

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, 237 of a random sample of 295 companies reported profits that had beaten estimates. Use this latest info to answer the following questions.

1A. Can you conclude the propotion of companies in the 4th quarter of 2012 that beat estimates is more than 73% at a=0.05? (please show all 7 steps)

1B. Construct a 98% confidence interval for the true propotion of companies in the 4th quarter of 2012 that beat estimates.

Explanation / Answer

a) H0: P = 0.73

    H1: P > 0.73

The test statistic z = (p - P)/sqrt(P * (1 - P)/n)

                              = (0.803 - 0.73)/sqrt(0.73 * 0.27/295)

                              = 2.82

P-value = P(Z > 2.82)

             = 1 - P(Z < 2.82)

             = 1 - 0.9976

             = 0.0024

As the p-value is less than the significance level (0.0024 < 0.05), so the null hypothesis is rejected.

So at alpha = 0.05, we can conclude that the proportion of companies in the 4th quarter of 2012 that beat estimates is more than 73%.

b) At 98% confidence interval the critical value z* = 2.33

The confidence interval is

p +/- z* sqrt(p * (1 - p)/n)

= 0.803 +/- 2.33 * sqrt(0.73 * (1 - 0.73)/295)

= 0.803 +/- 0.06

= 0.743, 0.863

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