A Random Sample of 19 Companies from the Forbes 500

question 10

Multiple Choice

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 Suppose the researchers test the hypotheses H₀: ₁ = 0, H_a: ₁ > 0. The P-value of the test is:

• A)greater than 0.10.
• B)between 0.10 and 0.05.
• C)between 0.05 and 0.01.
• D)less than 0.01.

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Definitions:

Statistical Significance

Statistical significance indicates the likelihood that a result from data collected and analyzed in a study is not due to chance, typically measured by a p-value.

Significance Level

A threshold in hypothesis testing that determines the probability level below which the null hypothesis is rejected, typically set at 0.05 or 5%.

Treatment

In research, treatment refers to any experimental condition applied to subjects or participants to observe its effect.

Significance

The likelihood that a result from data collected during research is not due to chance.