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

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