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.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station |
1 |
2 |
3 |
4 |
5 |

January |
135 | 124 | 128 | 64 | 78 |

April |
108 | 111 | 100 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let *d* = January − April.)

(a) What is the level of significance?
*H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} < 0; left-tailed*H*_{0}: ?_{d} > 0; *H*_{1}: ?_{d} = 0; right-tailed *H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} > 0; right-tailed*H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} ≠ 0; two-tailed
*P*-value > 0.2500.125 < *P*-value < 0.250 0.050 < *P*-value < 0.1250.025 < *P*-value < 0.0500.005 < *P*-value < 0.025*P*-value < 0.005

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that *d* has an approximately normal distribution.The standard normal. We assume that *d* has an approximately uniform 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.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the *P*-value.

Sketch the sampling distribution and show the area corresponding to the *P*-value.

(d) 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 ??

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) State your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January.Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.

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.

In the following data pairs, *A* represents birth rate and *B* represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.

A: |
12.5 | 13.2 | 12.6 | 12.1 | 11.4 | 11.1 | 14.2 | 15.1 |

B: |
9.6 | 14.3 | 10.7 | 14.2 | 13.2 | 12.9 | 10.9 | 10.0 |

A: |
12.5 | 12.3 | 13.1 | 15.8 | 10.3 | 12.7 | 11.1 | 15.7 |

B: |
14.1 | 13.6 | 9.1 | 10.2 | 17.9 | 11.8 | 7.0 | 9.2 |

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 increasefor company |
24 | 25 | 27 | 18 | 6 | 4 | 21 | 37 |
---|---|---|---|---|---|---|---|---|

A: Percent increasefor 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*.)

State the null and alternate hypotheses.

What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that *d* has an approximately normal distribution.

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 Student’s *t*. We assume that *d* has an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Find (or estimate) the *P*-value.

0.250 < *P*-value < 0.500

0.100 < *P*-value < 0.250

0.050 < *P*-value < 0.100

0.010 < *P*-value < 0.050

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 fail to reject *H*_{0}. The data are not statistically significant.

Since the *P*-value ≤ ?, we reject *H*_{0}. The data are statistically significant.

Since the *P*-value ≤ ?, we fail to reject *H*_{0}. The data are statistically significant.

Since the *P*-value > ?, we reject *H*_{0}. The data are not statistically significant.

Interpret your conclusion in the context of the application.

Fail to reject *H*_{0}. 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 *H*_{0}. 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 *H*_{0}. 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 *H*_{0}. 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.

*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.

A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian Reservation. The following table is the result of a random sample of eight regions on the Navajo Reservation.

Area on Navajo Reservation |
Number of Inhabited Houses |
Number of Inhabited Hogans |

Bitter Springs | 16 | 15 |

Rainbow Lodge | 18 | 12 |

Kayenta | 66 | 44 |

Red Mesa | 9 | 32 |

Black Mesa | 11 | 15 |

Canyon de Chelly | 28 | 47 |

Cedar Point | 50 | 17 |

Burnt Water | 50 | 18 |

Does this information indicate that the population mean number of inhabited houses is greater than that of hogans on the Navajo Reservation? Use a 5% level of significance. (Let *d* = houses − hogans.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

*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.

Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Wilderness District |
1 |
2 |
3 |
4 |
5 |

January |
122 | 122 | 130 | 64 | 78 |

April |
114 | 115 | 114 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. Solve the problem using the critical region method of testing. (Let *d* = January − April. Round your answers to three decimal places.)

test statistic | = | |

critical value | = |

*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 increasefor company |
12 | 8 | 10 | 18 | 6 | 4 | 21 | 37 |

A: Percent increasefor CEO |
19 | 27 | 21 | 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. Solve the problem using the critical region method of testing. (Let *d* = *B* − *A*. Round your answers to three decimal places.)

test statistic | = | |

critical value | = ± |

*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.

In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of four rats was given a reward of one food pellet each time they climbed a ladder. A second group of four rats was given a reward of five food pellets each time they climbed a ladder. On day 2, the groups were reversed, so the first group now got five food pellets for each climb and the second group got only one pellet for climbing the same ladder. The average times in seconds for each rat to climb the ladder 30 times are shown in the following table.

Rat |
A |
B |
C |
D |
E |
F |
G |
H |

Time 1 pellet |
12.1 | 13.7 | 11.2 | 12.1 | 11.0 | 10.4 | 14.6 | 12.3 |

Time 5 pellets |
11.3 | 12.2 | 12.0 | 10.6 | 11.5 | 10.5 | 12.9 | 11.0 |

What is the value of the sample test statistic? (Round your answer to three decimal places.)

*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.

In the following data pairs, *A* represents birth rate and *B* represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.

A: |
12.5 | 13.2 | 12.6 | 12.1 | 11.4 | 11.1 | 14.2 | 15.1 |

B: |
9.6 | 14.3 | 10.7 | 14.2 | 13.2 | 12.9 | 10.9 | 10.0 |

A: |
12.5 | 12.3 | 13.1 | 15.8 | 10.3 | 12.7 | 11.1 | 15.7 |

B: |
14.1 | 13.6 | 9.1 | 10.2 | 17.9 | 11.8 | 7.0 | 9.2 |

*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.

Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Wilderness District |
1 |
2 |
3 |
4 |
5 |

January |
128 | 127 | 137 | 64 | 78 |

April |
101 | 105 | 107 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. Solve the problem using the critical region method of testing. (Let *d* = January − April. Round your answers to three decimal places.)

test statistic | = | |

critical value | = |

*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.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station |
1 |
2 |
3 |
4 |
5 |

January |
135 | 122 | 128 | 64 | 78 |

April |
108 | 115 | 102 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let *d* = January − April.)

(a) What is the level of significance?
*H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} < 0; left-tailed*H*_{0}: ?_{d} > 0; *H*_{1}: ?_{d} = 0; right-tailed *H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} > 0; right-tailed*H*_{0}: ?_{d} = 0; *H*_{1}: ?_{d} ≠ 0; two-tailed
*P*-value > 0.2500.125 < *P*-value < 0.250 0.050 < *P*-value < 0.1250.025 < *P*-value < 0.0500.005 < *P*-value < 0.025*P*-value < 0.005

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

(b) What sampling distribution will you use? What assumptions are you making?

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.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the *P*-value.

Sketch the sampling distribution and show the area corresponding to the *P*-value.

(d) 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 ??

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January.Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.

*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.

Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Wilderness District |
1 |
2 |
3 |
4 |
5 |

January |
128 | 124 | 124 | 64 | 78 |

April |
114 | 96 | 113 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. Solve the problem using the critical region method of testing. (Let *d* = January − April. Round your answers to three decimal places.)

test statistic | = | |

critical value | = |

*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.

In the following data pairs, *A* represents birth rate and *B* represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.

A: |
12.5 | 13.2 | 12.6 | 12.1 | 11.4 | 11.1 | 14.2 | 15.1 |

B: |
9.6 | 14.3 | 10.7 | 14.2 | 13.2 | 12.9 | 10.9 | 10.0 |

A: |
12.5 | 12.3 | 13.1 | 15.8 | 10.3 | 12.7 | 11.1 | 15.7 |

B: |
14.1 | 13.6 | 9.1 | 10.2 | 17.9 | 11.8 | 7.0 | 9.2 |

Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use ? = 0.01. (Let *d* = *A* − *B*.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

*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.

The artifact frequency for an excavation of a kiva in Bandelier National Monument gave the following information.

Stratum |
Flaked Stone Tools |
Nonflaked Stone Tools |

1 | 10 | 2 |

2 | 10 | 3 |

3 | 9 | 2 |

4 | 1 | 3 |

5 | 4 | 7 |

6 | 38 | 32 |

7 | 51 | 30 |

8 | 25 | 12 |

What is the value of the sample test statistic? (Round your answer to three decimal places.)

*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.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station |
1 |
2 |
3 |
4 |
5 |

January |
137 | 124 | 128 | 64 | 78 |

April |
104 | 115 | 102 | 88 | 61 |

Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let *d* = January − April.)

(a) What is the level of significance?

What is the value of the sample test statistic?

*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.

In the following data pairs, *A* represents the cost of living index for housing and *B* represents the cost of living index for groceries. The data are paired by metropolitan areas in the United States. A random sample of 36 metropolitan areas gave the following information.

A: |
132 | 109 | 126 | 124 | 102 | 96 | 100 | 131 | 97 |

B: |
127 | 118 | 139 | 102 | 103 | 107 | 109 | 117 | 105 |

A: |
120 | 115 | 98 | 111 | 93 | 97 | 111 | 110 | 92 |

B: |
110 | 109 | 105 | 109 | 104 | 102 | 100 | 106 | 103 |

A: |
85 | 109 | 123 | 115 | 107 | 96 | 108 | 104 | 128 |

B: |
98 | 102 | 100 | 95 | 93 | 98 | 93 | 90 | 108 |

A: |
121 | 85 | 91 | 115 | 114 | 86 | 115 | 90 | 113 |

B: |
102 | 96 | 92 | 108 | 117 | 109 | 107 | 100 | 95 |

What is the value of the sample test statistic? (Round your answer to three decimal places.)

*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.

Wilderness District |
1 |
2 |
3 |
4 |
5 |

January |
138 | 131 | 131 | 64 | 78 |

April |
115 | 103 | 101 | 88 | 61 |

*d* = January − April. Round your answers to three decimal places.)

test statistic | = | ? |

critical value | = | ? |

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