A Large National Bank Charges Local Companies for Using Their $( y )$

Multiple Choice

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges $( y )$ , measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue $( x )$ , measured in $\$$ million. Data for 21 companies who use the bank's services were used to fit the model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$
Suppose a $95 \%$ confidence interval for $\beta 1$ is $( 15,25 )$ . Interpret the interval.

A) We are $95 \%$ confident that service charge $( y )$ will decrease between $\$ 15$ and $\$ 25$ for every $\$ 1$ million increase in sales revenue $( x )$ .
B) We are $95 \%$ confident that sales revenue $( x )$ will increase between $\$ 15$ and $\$ 25$ million for every $\$ 1$ increase in service charge $( y )$ .
C) We are $95 \%$ confident that service charge $( y )$ will increase between $\$ 15$ and $\$ 25$ for every $\$ 1$ million increase in sales revenue $( x )$ .
D) We are $95 \%$ confident that the mean service charge will fall between $\$ 15$ and $\$ 25$ per month.