Deck 10: Inferences About Differences

Question 1

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 that a random sample of companies yielded the following data: $$\begin{array} { l | l l l l l l l l } \hline \text { B : Percent for company } & 13 & 29 & 17 & 7 & 28 & 16 & 28 & 16 \\\hline \text { A: Percent for CEO } & 12 & 31 & 14 & 7 & 32 & 16 & 19 & 19 \\\hline\end{array}$$ 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 10% level of significance. What is the value of the test statistic?

A)0.322
B)-0.344
C)-0.322
D)-0.368
E)0.344

Answer 1

0.344

Question 2

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 that a random sample of companies yielded the following data: $$\begin{array} { l | c c c c c c c c } \hline \text { B : Percent for company } & 18 & 8 & 7 & 6 & 10 & 23 & 23 & 26 \\\hline \text { A: Percent for CEO } & 19 & 10 & 6 & - 2 & 10 & 20 & 19 & 20 \\\hline\end{array}$$ 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 10% level of significance. What does the area of the sampling distribution corresponding to your P-value look like if the test statistic t = 1.918?

A)shade are to the left of -1.918
B)shade are to the left of -1.918 and to the right of 1.918
C)shade are to the right of -1.918 and to the left of 1.918
D)shade are to the right of 1.918

Answer 2

shade are to the left of -1.918 and to the right of 1.918

Question 3

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 that a random sample of companies yielded the following data: $$\begin{array} { l | l l l l l l l l } \hline \text { B : Percent for company } & 13 & 10 & 29 & 14 & 13 & 21 & 11 & 14 \\\hline \text { A: Percent for CEO } & 17 & 7 & 34 & 4 & 3 & 21 & 10 & 15 \\\hline\end{array}$$ 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 1% level of significance. Are the data statistically significant at level $\alpha$ ? Will you reject or fail to reject the null hypothesis?

A)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 reject the null hypothesis.
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 null hypothesis.
C)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.
D)Since the interval containing the P-values has values that are larger than the level of significance, the data are statistically significant and so we fail to reject the null hypothesis.

Answer 3

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.

Question 4

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 that a random sample of companies yielded the following data: $$\begin{array} { l | l l l l l l l l } \text { B: Percent for company } & 23 & 22 & 25 & 19 & 20 & 28 & 8 & 27 \\\hline \text { A: Percent for CEO } & 13 & 16 & 22 & 22 & 16 & 33 & 8 & 21 \\\hline\end{array}$$ 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 10% level of significance. What is $\alpha$ ?

A)0.050
B)0.800
C)0.200
D)0.900
E)0.100

Question 5

A random sample of 16 communities in western Kansas gave the following information for people under 25 years of age. $n _ { 1 } =$ Rate of hay fever per 1000 population for people under 25
$x _ { 1 } :$ $\begin{array} { l l l l l l l l l l l l l l l l } 115 & 113 & 111 & 111 & 151 & 112 & 111 & 120 & 109 & 123 & 121 & 121 & 124 & 115 & 108 & 122\end{array}$ A random sample of 14 regions in western Kansas gave the following information for people over 50 years old.
$n _ { 2 } =$ Rate of hay fever per 1000 population for people over 50
$x _ { 2 }$ 107 $\quad$ 107 $\quad$ 100 $\quad$ 99 $\quad$ 102 $\quad$ 105 $\quad$ 98 $\quad$ 81 $\quad$ 104 $\quad$ 104 $\quad$ 110 $\quad$ 97 $\quad$ 117 $\quad$ 97 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $\alpha$ = 0.05. What is the level of significance?

A)0.975
B)0.050
C)0.025
D)0.100
E)0.950

Question 6

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 that a random sample of companies yielded the following data: $$\begin{array} { | l | l l l l l l l l } \hline \text { B : Percent for company } & 11 & 28 & 8 & 16 & 29 & 24 & 13 & 23 \\\hline \text { A: Percent for CEO } & 16 & 33 & 3 & 13 & 22 & 24 & 5 & 18 \\\hline\end{array}$$ 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 10% level of significance. Find (or estimate) the P-value.

A)0.40 < P-value < 0.50
B)0.20 < P-value < 0.40
C)0.02 < P-value < 0.05
D)0.10 < P-value < 0.20

Question 7

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 that a random sample of companies yielded the following data: $$\begin{array} { l | l l l l l l l l } \hline \text { B : Percent for company } & 2 & 5 & 29 & 8 & 21 & 14 & 13 & 12 \\\hline \text { A: Percent for CEO } & - 1 & 5 & 21 & 13 & 12 & 18 & 9 & 8 \\\hline\end{array}$$ 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 1% level of significance. Will you use a left tailed, right tailed, or two tailed test?

A)left tailed test
B)two tailed test
C)right tailed test

Question 8

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 that a random sample of companies yielded the following data: $$\begin{array} { | l | l l l l l l l l } \text { B: Percent for company } & 19 & 13 & 2 & 14 & 12 & 25 & 20 & 9 \\\hline \text { A: Percent for CEO } & 19 & 8 & 4 & 4 & 14 & 18 & 17 & 3 \\\hline\end{array}$$ 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 10% level of significance. What is the alternate hypothesis?

A)H₁ : $\mu$ _$\partial$ $\gt$ 0
B)H₁ : $\mu$ _$\partial$ =0
C)H₁ : $\mu$ _$\partial$ $\neq$ 0
D)H₁ : $\mu$ _$\partial$ <0

Question 9

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age. x₁: Rate of hay fever per 1000 population for people under 25
121 110 90 82 124 112 102 91 122 112 114 108 112 81 122 142 A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.
X₂: Rate of hay fever per 1000 population for people over 50
110 88 126 87 112 73 100 94 92 100 102 102 89 90 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use 0.05. What is the value of the test statistic?
$$\alpha =$$

A)-0.550
B)2.141
C)-1.519
D)0.550
E)-2.141

Question 10

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age. x₁: Rate of hay fever per 1000 population for people under 25
116 136 96 98 81 81 128 95 122 122 107 91 116 122 101 116 A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.
X₂: Rate of hay fever per 1000 population for people over 50
105 107 86 100 106 103 85 102 106 99 127 100 109 100 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use 0.05. If 0.10 < P-value < 0.20, will you reject or fail to reject the null hypothesis? Are the data statistically significant at confidence level $\alpha$ ?
$$\alpha =$$

A)Since the P-value is less than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.
B)Since the P-value is less than the level of significance, the data are not statistically significant. Thus, we reject the null hypothesis.
C)Since the P-value is greater than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.
D)Since the P-value is greater than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis.
E)Since the P-value is less than the level of significance, the data are statistically significant. Thus, we reject the null hypothesis.

Question 11

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age. x₁: Rate of hay fever per 1000 population for people under 25
124 114 124 130 145 109 115 98 134 124 122 112 145 121 96 112 A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.
X₂: Rate of hay fever per 1000 population for people over 50
108 92 107 99 106 86 106 107 112 104 73 96 96 104 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use 0.05. Find (or estimate) the P-value.
$$\alpha =$$

A)P-value < 0.005
B)0.01 < P-value < 0.025
C)P-value > 0.20
D)0.005 < P-value < 0.01
E)0.10 < P-value < 0.20