A random sample of 19 companies from the Forbes 500 list was selected, and the r

Question

A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: Profits = + (Sales) where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. r2 = 0.662 s = 466.2 Parameter Parameter estimate Std. err. of parameter est. –176.644 61.16 0.092498 0.0075 Suppose the researchers test the hypotheses H0: 1 = 0, Ha: 1 > 0. The P-value of the test is A. between 0.10 and 0.05. B. between 0.05 and 0.01. C. less than 0.01. D. greater than 0.10.

Explanation / Answer

Here, n=sample size=19,

1^=0.092498 & standard error of  1^=SE(^)=0.0075

We have to test here H0: 1 = 0, Ha: 1 > 0.

Test statistic for testing above hypothesis is ,

t0=1^ / SE(1^)

=0.092498/ 0.0075

=12.33307

P-value=P(tn-2>t0)=P(t17>12.33307)=3.305837e-10

Hence , answer of this question is option  C. less than 0.01.

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