Question

Asian economies impact some of the world's largest populations.
The growth of an economy has a big influence on the everyday lives
of ordinary people. Are Asian economies changing? A random sample
of 15 Asian economies gave the following information about annual
percentage growth rate. (Reference: *Handbook of International
Economic Statistics*, U.S. Government Documents.)

Region |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |

Modern
Growth Rate % |
4.9 | 2.5 | 7.6 | 2.1 | 0.9 | 5.9 | 2.5 | 4.5 |

Historic
Growth Rate |
3.4 | 1.5 | 7.7 | 5.3 | 3.7 | 6.4 | 3.1 | 8.8 |

Region |
9 |
10 |
11 |
12 |
13 |
14 |
15 |

Modern
Growth Rate % |
4.3 | 5.9 | 6.6 | 3.1 | 3.8 | 0.4 | 7.9 |

Historic
Growth Rate |
6.2 | 7.3 | 6.6 | 1.7 | 1.7 | 2.7 |
5.9 |

(b) Compute the sample test statistic. (Use 2 decimal
places.)

(c) Find the *P*-value of the sample test statistic. (Use 4
decimal places.)

The Focus Problem at the beginning of this chapter asks you to use a sign test with a 5% level of significance to test the claim that the overall temperature distribution of Madison, Wisconsin, is different (either way) from that of Juneau, Alaska. The monthly average data (in °F) are as follows.

Month |
Jan. |
Feb. |
March |
April |
May |
June |

Madison |
17.3 | 21.7 | 31.6 | 46.2 | 57.9 | 67.2 |

Juneau |
22.9 | 27.1 | 31.1 | 38.8 | 46.9 | 52.4 |

Month |
July |
Aug. |
Sept. |
Oct. |
Nov. |
Dec. |

Madison |
71.4 | 69.2 | 60.4 | 51.5 | 35.5 | 22.2 |

Juneau |
55.1 | 54.5 | 49.2 | 41.7 | 32.7 |
26.7 |

(b) Compute the sample test statistic. (Use 2 decimal
places.)

(c) Find the *P*-value of the sample test statistic. (Use 4
decimal places.)

Are yields for organic farming different from conventional
farming yields? Independent random samples from method A (organic
farming) and method B (conventional farming) gave the following
information about yield of lima beans (in tons/acre). (Reference:
*Agricultural Statistics*, United States Department of
Agriculture.)

Method
A |
2.14 | 2.03 | 1.22 | 1.13 | 2.27 | 1.34 | 1.66 | 1.40 | 2.01 | 1.67 | 1.68 | |

Method
B |
1.92 | 1.29 | 1.16 | 1.74 | 1.56 | 1.59 | 1.45 | 1.84 | 2.33 | 2.12 | 2.09 | 1.39 |

(b) Compute the sample test statistic. (Use 2 decimal
places.)

(c) Find the *P*-value of the sample test statistic. (Use 4
decimal places.)

Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of sweet corn (in tons/acre).

Method
A |
5.87 | 6.69 | 6.38 | 5.84 | 6.30 | 6.77 | 6.13 | 6.49 | 6.16 | 5.82 | 6.65 | 5.93 |

Method
B |
6.57 | 6.28 | 6.42 | 6.56 | 5.98 | 5.78 | 6.18 | 5.94 | 6.45 | 5.74 | 6.74 |

(c) Find the *P*-value of the sample test statistic. (Use 4
decimal places.)

Answer #1

(a)

Here we have two independent samples so independent sample t test will be used.

Hypotheses are:

Following is the output of descriptive statistics generated by excel:

Descriptive statistics | ||

Modern growth rate, X | Historic growth rate, Y | |

count | 15 | 15 |

mean | 4.193 | 4.800 |

sample standard deviation | 2.303 | 2.397 |

sample variance | 5.305 | 5.747 |

minimum | 0.4 | 1.5 |

maximum | 7.9 | 8.8 |

range | 7.5 | 7.3 |

Here we have following information:

Pooled standard deviation is :

and t-statistics will be

(b)

Here degree of feedom will be

Test is two tailed so p-value using excel function "=TDIST(0.71,28,2)" is 0.4836.

Since p-value is large so we fail to reject the null hypothesis.

Asian economies impact some of the world's largest populations.
The growth of an economy has a big influence on the everyday lives
of ordinary people. Are Asian economies changing? A random sample
of 15 Asian economies gave the following information about annual
percentage growth rate. (Reference: Handbook of International
Economic Statistics, U.S. Government Documents.)
Region
1
2
3
4
5
6
7
8
Modern
Growth Rate %
4.2
2.7
7.4
2.6
0.8
5.3
2.6
4.8
Historic
Growth Rate
3.1
1.3...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets. A random sample of leading companies in France gave
the following percentage yields based on assets. 4.3 5.9 3.2 3.5
2.3 3.5 2.8 4.4 5.7 3.4 4.1 6.8 2.9 3.2 7.2 6.5 5.0 3.3 2.8 2.5 4.5
Use a calculator to verify that the sample variance is s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.6
5.6
3.4
3.9
2.7
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

The Focus Problem at the beginning of this chapter asks you to
use a sign test with a 5% level of significance to test the claim
that the overall temperature distribution of Madison, Wisconsin, is
different (either way) from that of Juneau, Alaska. The monthly
average data (in °F) are as follows.
Month
Jan.
Feb.
March
April
May
June
Madison
17.4
21.9
31.4
46.7
57.9
67.5
Juneau
22.3
27.8
31.7
38.5
46.7
52.6
Month
July
Aug.
Sept.
Oct.
Nov.
Dec....

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.2
5.3
3.4
3.1
2.7
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.2
5.4
3.2
3.4
2.9
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.2
5.3
3.1
3.9
2.4
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.7
5.2
3.6
3.7
2.1
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.6
5.1
3.1
3.8
2.9
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

An economist wonders if corporate productivity in some countries
is more volatile than in other countries. One measure of a
company's productivity is annual percentage yield based on total
company assets.
A random sample of leading companies in France gave the following
percentage yields based on assets.
4.2
5.2
3.7
3.9
2.5
3.5
2.8
4.4
5.7
3.4
4.1
6.8
2.9
3.2
7.2
6.5
5.0
3.3
2.8
2.5
4.5
Use a calculator to verify that the sample variance is
s2 ≈...

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