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. A. Calculate the following: x (with a bar on top of it), y (with a bar on top of it), and s subscript y. B. State the decision rule for 0.01 significance level: H₀: ? ? 0; H₁: ? < 0. Reject H0 if t < ?. C. Compute the value of the test statistic.

Answer 1

Solution :

The table given shows the number of cars (in millions) sold in the United States for various years and the percent of those cars manufactured by GM.

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A) To calculate   :

The mean and standard deviation of a set of sample values is given as ,

Thus , we have from the data ,

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B and C) The hypothesis of interest is given as ,

The test statistic for the above test is given as ,

We Reject H₀ at level of significance iff ,

Calculations : From the data , we have the following information :

The value of the test statisti is   .................................................. (Ans)

Clearly , we can see that ,

Conclusion : Since , , thus , we REJECT the null hypothesis H₀ at 0.01 level of significance and conclude on the basis of the given data that the relationship between the X and the Y points is Statistically Significant from 0 (zero).

That is , the correlation the number of cars (in millions) sold in the United States for various years and the percent of those cars manufactured by GM is NEGATIVE.

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