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) 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 b) Sketch the sampling distribution and show the area corresponding to the P-value. c) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? -Since the P-value > ?, we reject H0. The data are not statistically significant. -Since the P-value ≤ ?, we reject H0. The data are statistically significant. -Since the P-value > ?, we fail to reject H0. The data are not statistically significant. -Since the P-value ≤ ?, we fail to reject H0. The data are statistically significant.
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) 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
b) Sketch the sampling distribution and show the area corresponding to the P-value.
c) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
-Since the P-value > ?, we reject H0. The data are not statistically significant.
-Since the P-value ≤ ?, we reject H0. The data are statistically significant.
-Since the P-value > ?, we fail to reject H0. The data are not statistically significant.
-Since the P-value ≤ ?, we fail to reject H0. The data are statistically significant.
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