Question

A large national bank charges local companies for using their services. A bank official reported the results of a regression to predict the bank charges (Y) -- measured in dollars per month-- for services rendered to local companies. One independent variable used to predict service charges is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the simple linear regression model and the results are provided below:

Y = -2,700 + 20X

p value = .034

Interpret the p value

There is sufficient evidence to conclude that sales revenue is a useful linear predictor of service charge

There is insufficient evidence to conclude that sales revenue is a useful linear predictor of service charge

Sales revenue is a poor predictor of service charge

For every 1 million increase in revenue, you expect the service charge to increase .034

Answer 1

Solution:

Given:

Data for 21 companies who use the bank's services were used to fit the simple linear regression model and the results are provided below:

Y = -2,700 + 20X

p value = 0.034

We have to interpret the p value.

Hypothesis are:

that is: slope coefficient is 0, means  sales revenue is not a useful linear predictor of service charge

Vs

, that is:  slope coefficient is not 0, means sales revenue is a useful linear predictor of service charge

Since level of signficance is not given, we assume it is:

Decision Rule:
Reject null hypothesis H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.034 < 0.05 level of significance, we reject null hypothesis H0 in favor of H1.

Thus correct answer is:

There is sufficient evidence to conclude that sales revenue is a useful linear predictor of service charge