Remaining Time: 2 hours, 50 minutes, 43 seconds. Question Completion Status: est
ID: 3327365 • Letter: R
Question
Remaining Time: 2 hours, 50 minutes, 43 seconds. Question Completion Status: estion 10 Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual com percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data 1 points Save Ans Percent for company Percent for CEO Do these data indicate that the population mean percentage increase in corporate revenue irow Bo is different from the population mean per 10 CEO salary? Use a 1% level of significance. Are the data statistically significant at level a? Will you reject or fail to reject the null hypothesis A. Since the interval containing the P-values has values that are larger than the level of significance, the data are statist B. Since the interval containing the P-values has values that are smaller than the level of significance, the data are statistically significant and so we reject the c. Since the interval containing the P-values has values that are larger than the level of significance, the data are mot statistically sign scant and so we fail to D. Since the interval containing the P-values has values that are smaller than the level of significance, the data are not statistically significant and so we fail to increase in reject the null hypothesis null hypothesis reject the null hypothesis reject the null hypothesis the null hypothesis significant and so we fail to E. Since the interval containing the P-values has values that are larger than the level of significance, t cBooExplanation / Answer
Null Hypothesis H0: The mean percentage increase in revenue of company is equal to mean annual percentage increase in salary of CEO's.
Alternative Hypothesis H1: The mean percentage increase in revenue of company is not equal to mean annual percentage increase in salary of CEO's.
The percentage increase in revenue of company are 13,10,29,14,13,21,11,14
The percentage increase in salary of CEO's are 17,7,34,4,3,21,10,15
The mean percentage increase in revenue of company is 15.625
The mean percentage increase in salary of CEO's are 13.875
The standard deviation of percentage increase in revenue of company, s1 = 6.323
The standard deviation of percentage increase in salary of CEO's, s2 = 10.316
For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(6.3232/8) + (10.3162/8] = 4.278
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
= (6.3232/8 + 10.3162/8)2 / { [ (6.3232 / 8)2 / (8 - 1) ] + [ (10.3162 / 8)2 / (8 - 1) ] }
= 12 (Rounding to nearest integer)
t = [ (x1 - x2) - d ] / SE = (15.625 - 13.875) / 4.278 = 0.409
P-value for t = 0.409 and df = 12 is 0.3449
For two tail test, P-value = 2 * 0.3449 = 0.6898 which is greater than the level of significance of 0.01.
So, the option C is correct. Since the interval containing the P-values has values that are larger than the level of significance, the data are not statistically significant and so we fail to reject the null hypothesis.