EXPLANATION: the T-Test Statistic Is $$t = \frac { \left( b _ { 1 } - \beta _ { 1 } \right) } { S _ { b _ { 1 } } } = \frac { ( 2.5 - 3 ) } { 0.3536 } = - 1.4142$$

Short Answer

EXPLANATION: The t-test statistic is $$t = \frac { \left( b _ { 1 } - \beta _ { 1 } \right) } { S _ { b _ { 1 } } } = \frac { ( 2.5 - 3 ) } { 0.3536 } = - 1.4142$$ KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows. $\begin{array}{ccc}\underline{\text { Broker }}&\underline{\text { Clients }} &\underline{\text { Sales }}\\1 & 27 & 52 \\2 & 11 & 37 \\3 & 42 & 64 \\4 & 33 & 55 \\5 & 15 & 29 \\6 & 15 & 34 \\7 & 25 & 58 \\8 & 36 & 59 \\9 & 28 & 44 \\10 & 30 & 48 \\11 & 17 & 31 \\12 & 22 & 38\end{array}$
-Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. The denominator of the test statistic is sb1 . The value of sb1
in this sample is ________.