In 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 25 18 6 4 21 37 A: Percent increase for CEO 21 23 22 14 −4 19 15 30 a) State the null and alternate hypotheses. select one: H0: ?d ≠ 0; H1: ?d = 0 H0: ?d = 0; H1: ?d ≠ 0 H0: ?d = 0; H1: ?d < 0 H0: ?d = 0; H1: ?d > 0 H0: ?d > 0; H1: ?d = 0 b) What sampling distribution will you use? What assumptions are you making? select one: 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. The Student's t. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately uniform distribution. c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
In 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 25 18 6 4 21 37
A: Percent increase
for CEO 21 23 22 14 −4 19 15 30
a) State the null and alternate hypotheses. select one:
H0: ?d ≠ 0; H1: ?d = 0
H0: ?d = 0; H1: ?d ≠ 0
H0: ?d = 0; H1: ?d < 0
H0: ?d = 0; H1: ?d > 0
H0: ?d > 0; H1: ?d = 0
b) What sampling distribution will you use? What assumptions are you making? select one:
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.
The Student's t. We assume that d has an approximately uniform distribution.
The standard normal. We assume that d has an approximately uniform distribution.
c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
We want to find the test statistic and hypothesis
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