To solve the problem using the critical region method of testing, we need to first calculate the differences between the percentages of CEO salary increase and corporate revenue increase:
d = B - A
d = (22 - 18), (6 - 18), (28 - 19), (18 - 14), (6 + 4), (4 - 19), (21 - 15), (37 - 30)
d = 4, -12, 9, 4, 10, -15, 6, 7
Next, we calculate the sample mean and sample standard deviation of d:
Mean (d) = ?d / n = (4 - 12 + 9 + 4 + 10 - 15 + 6 + 7) / 8 = 3/8 = 0.375
s = ?[?(d - Mean(d))^2 / (n - 1)] = ?[152.125 / 7] = 2.403
Using a 5% level of significance, we need to find the critical value for a two-tailed test with 7 degrees of freedom. We can find this value by looking up the t-distribution table or using a calculator. The critical value is \approx imately ± 2.365.
The test statistic for the difference in population mean percentage increases is:
t = Mean(d) / (s / ?n) = 0.375 / (2.403 / ?8) = 0.782
Since our test statistic of 0.782 is less than the critical value of ±2.365, we fail to reject the null hypothesis. This means that there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary.
Comparing our conclusion with the conclusion obtained by using the P-value method, we find that they are the same. The P-value for our test is \approx imately 0.454, which is greater than 0.05 (our level of significance). Therefore, we fail to reject the null hypothesis using the P-value method as well.
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