Question

The following data are paired by date. Let x and y be random variables representing wind direction at 5 a.m. and 5 p.m., respectively (units are degrees on a compass, with 0° representing true north). The readings were taken at seeding level in a cloud seeding experiment. A random sample of days gave the following information. x 178 140 197 224 54 175 257 72 172 y 148 142 217 125 49 245 218 35 147 x 207 265 110 193 180 190 94 8 91 y 213 218 100 170 245 117 140 99 62 Use the sign test with a 5% level of significance to test the claim that the distributions of wind directions at 5 a.m. and 5 p.m. are different. Interpret the results. What is the level of significance? State the null and alternate hypotheses. H0: Distributions are the same. H1: Distributions are different. H0: Distributions are different. H1: Distributions are different. H0: Distributions are the same. H1: Distributions are the same. H0: Distributions are different. H1: Distributions are the same. Compute the sample test statistic. (Round your answer to two decimal places.) What sampling distribution will you use? Student's t normal chi-square uniform Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer #1

H0: Distributions are the same

H1: Distributions are the different

Form the given data

S.No. | X | Y | Diff = X-Y |

1 | 178 | 148 | 30 |

2 | 140 | 142 | -2 |

3 | 197 | 217 | -20 |

4 | 224 | 125 | 99 |

5 | 54 | 49 | 5 |

6 | 175 | 245 | -70 |

7 | 257 | 218 | 39 |

8 | 72 | 35 | 37 |

9 | 172 | 147 | 25 |

10 | 207 | 213 | -6 |

11 | 265 | 218 | 47 |

12 | 110 | 100 | 10 |

13 | 193 | 170 | 23 |

14 | 180 | 245 | -65 |

15 | 190 | 117 | 73 |

16 | 94 | 140 | -46 |

17 | 8 | 99 | -91 |

18 | 91 | 62 | 29 |

S+ = | number of +ve signs |

= | 11 |

S- = | 7 |

Thus we conclude that Distributions are different

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below. Type of Household Percent of U.S. Households Observed Number
of Households in the Community Married with children 26% 93
Married, no children 29% 112 Single parent 9% 34 One person 25% 103
Other (e.g., roommates, siblings) 11% 69 Use a 5% level of
significance to test the claim that the distribution of U.S.
households fits the...

Benford's Law states that the first nonzero digits of numbers
drawn at random from a large complex data file have the following
probability distribution.† First Nonzero Digit 1 2 3 4 5 6 7 8 9
Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046
Suppose that n = 275 numerical entries were drawn at random from a
large accounting file of a major corporation. The first nonzero
digits were recorded for the sample. First Nonzero Digit 1 2...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
96
Married, no children
29%
113
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
73
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
104
Married, no children
29%
112
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
93
Married, no children
29%
127
Single parent
9%
35
One person
25%
88
Other (e.g., roommates, siblings)
11%
68
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
98
Married, no children
29%
118
Single parent
9%
38
One person
25%
91
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of
Household
Percent of
U.S.
Households
Observed
Number
of Households in
the Community
Married with children
26%
105
Married, no children
29%
120
Single parent
9%
28
One person
25%
91
Other (e.g., roommates, siblings)
11%
67
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The age distribution of the Canadian population and the age
distribution of a random sample of 455 residents in the Indian
community of a village are shown below.
Age
(years)
Percent of
Canadian Population
Observed
Number
in the Village
Under 5
7.2%
45
5 to 14
13.6%
83
15 to 64
67.1%
280
65 and older
12.1%
47
Use a 5% level of significance to test the claim that the age
distribution of the general Canadian population fits the age...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
92
Married, no children
29%
120
Single parent
9%
29
One person
25%
101
Other (e.g., roommates,
siblings)
11%
69
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The age distribution of the Canadian population and the age
distribution of a random sample of 455 residents in the Indian
community of a village are shown below.
Age
(years)
Percent of
Canadian Population
Observed
Number
in the Village
Under 5
7.2%
45
5 to 14
13.6%
74
15 to 64
67.1%
286
65 and older
12.1%
50
Use a 5% level of significance to test the claim that the age
distribution of the general Canadian population fits the age...

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