Question

The table below shows the number of cars (in millions) sold in the United States for various years and the percent of those cars manufactured by GM. Year Cars Sold (millions) Percent GM Year Cars Sold (millions) Percent GM 1950 6.0 50.2 1985 15.4 40.1 1955 7.8 50.4 1990 13.5 36.0 1960 7.3 44.0 1995 15.5 31.7 1965 10.3 49.9 2000 17.4 28.6 1970 10.1 39.5 2005 16.9 26.9 1975 10.8 43.1 2010 11.6 19.1 1980 11.5 44.0 2015 17.5 17.6 Use a statistical software package to answer the following questions.

x¯
y¯
Sx
Sy
r

A. State the decision rule for 0.01 significance level: H0: ? ? 0; H1: ? < 0. REJECT H0 IF T < ?

B. Compute the value of the test statistic.

Answer 1

Year	Cars sold, x	Percent GM, y	(x-xbar)	(y - ybar)	(x-xbar)*(y - ybar)	(x-xbar)²	(y - ybar)²
1950	6	50.2	-6.26	12.98	-81.21	39.15	168.44
1955	7.8	50.4	-4.46	13.18	-58.74	19.87	173.67
1960	7.3	44	-4.96	6.78	-33.60	24.57	45.95
1965	10.3	49.9	-1.96	12.68	-24.81	3.83	160.75
1970	10.1	39.5	-2.16	2.28	-4.92	4.65	5.19
1975	10.8	43.1	-1.46	5.88	-8.57	2.12	34.56
1980	11.5	44	-0.76	6.78	-5.13	0.57	45.95
1985	15.4	40.1	3.14	2.88	9.05	9.88	8.29
1990	13.5	36	1.24	-1.22	-1.52	1.54	1.49
1995	15.5	31.7	3.24	-5.52	-17.91	10.52	30.49
2000	17.4	28.6	5.14	-8.62	-44.34	26.45	74.33
2005	16.9	26.9	4.64	-10.32	-47.92	21.56	106.53
2010	11.6	19.1	-0.66	-18.12	11.91	0.43	328.39
2015	17.5	17.6	5.24	-19.62	-102.87	27.49	385.00
	xbar	ybar	Σ (x-xbar)	Σ (y - ybar)	Σ (x-xbar)*(y - ybar)	Σ (x-xbar)²	Σ (y - ybar)²
	12.26	37.22	0.00	0.00	-410.58	192.63	1569.02
r	-0.74682

A. State the decision rule for 0.01 significance level: H0: ? ? 0; H1: ? < 0. REJECT H0 IF T < ?

REJECT H0 IF T < 3.054

B. Compute the value of the test statistic.

t = r*(√n-2/1-r²)

t = -0.747*(√14 - 2/1-0.747²)

t = -3.89