n this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. 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 company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increase for company 24 25 27 18 6 4 21 37 A: Percent increase for CEO 21 23 24 14 −4 19 15 30 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Let d = B − A.) What is the value of the sample test statistic? (Round your answer to three decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. State the null and alternate hypotheses. H0: μd > 0; H1: μd = 0 H0: μd = 0; H1: μd > 0 H0: μd = 0; H1: μd ≠ 0 H0: μd ≠ 0; H1: μd = 0 H0: μd = 0; H1: μd < 0 What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately normal distribution.The Student's t. We assume that d has an approximately normal distribution. Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Based on your answers, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? Since the P-value > α, we fail to reject H0. The data are not statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant. Since the P-value ≤ α, we reject H0. The data are statistically significant. Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. (c) Interpret your conclusion in the context of the application. Fail to reject H0. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Fail to reject H0. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject H0. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject H0. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
B: Percent increase for company |
24 | 25 | 27 | 18 | 6 | 4 | 21 | 37 |
---|---|---|---|---|---|---|---|---|
A: Percent increase for CEO |
21 | 23 | 24 | 14 | −4 | 19 | 15 | 30 |
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