1 answer

QUESTION 5 3)-7) The mangers of a brokerage firm are interested in finding out if the...

Question:

QUESTION 5 3)-7) The mangers of a brokerage firm are interested in finding out if the number of new clients a broker brings i
QUESTION 5 3)-7) The mangers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales (in 1,000 $) generated by the broker. They sampled 25 brokers and determine the number of new clients they have enrolled in the last year and the data are partially presented in the table with the following results: y = 25.5+1.35X, SST=1430, SSR=1188.55, and --(x - 2)2-102. Broker Clients (X) Sales (M) 1 26 60 2 23 57 - 25 24 59 At 5% level of significance, which of the following represents the results of the relevant hypothesis test? fail to reject HO no decision no test reject HO

Answers

We are given regression equation :

1596053130551_blob.png = 25.5 + 1.35*x

So b0 = 25.5 and b1 = 1.35

n = 25

SSE = SST - SSR = 1430 - 1188.55  

SSE = 241.45

H0 : β1 = 0 vs Ha : β1 ≠0

Test statistic :

t = \frac{b_1}{\sqrt{SSE/(n-2)*\sum (x-\bar{x})^2}}

= \frac{1.35}{\sqrt{241.45/(25-2)*102}}

t = 1.35 / 0.3208

t = 4.21

Critical value :  α = 0.05 and df = n -2 = 23

For two tail area 0.05 and df = 23 , critical value is 2.069 --- ( from t distribution table )

As | t | is greater than 2.069 , We reject the null hypothesis

Answer : reject H0

.

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