Question

Income (in 1960 dollars/person) for European countries and the percent of the labor force (in %) that works in agriculture in 1960 are in the table below ('OECD economic development,' 2013). Test at the 8% level for a negative correlation between percent of labor in agriculture and income of European countries.

percent of labor in agriculture	income
15	1035
36	529
42	290
44	238
11	1361
11	810
25	839
20	977
27	504
20	1013
18	1049
56	324
23	681
79	177
4	1105

What is H0:

What is HA:

Test statistic, t=

t=r√(1−(r)2(n−2))t=r(1-(r)2(n-2)) =

Make a decision

State a conclusion

Answer 1

Sample correlation coefficient :

x: percent of labor in agriculture	y:income	xy	x2	y2
15	1035	15525	225	1071225
36	529	19044	1296	279841
42	290	12180	1764	84100
44	238	10472	1936	56644
11	1361	14971	121	1852321
11	810	8910	121	656100
25	839	20975	625	703921
20	977	19540	400	954529
27	504	13608	729	254016
20	1013	20260	400	1026169
18	1049	18882	324	1100401
56	324	18144	3136	104976
23	681	15663	529	463761
79	177	13983	6241	31329
4	1105	4420	16	1221025
=431	=10932	=226577	=17863	=9860358

Sample correlation coefficient : r=-0.8595

Null hypothesis : H_o : There is no Correlation Coefficient : = 0

Alternate Hypothesis : H_a : There is negative correlation : < 0

Left tailed test

Test Statistic : t

Degrees of freedom = n-2 = 15-2=13

For 13 degrees of freedom , P(t<-6.0629) = 0.0000

Level of significance :8% : 0.08

As p-value:0.0000 less than level of significance (0.08) reject the null hypothesis.

There is sufficient evidence to conclude that there is negative correlation between percent of labor in agriculture and income of European countries.