Question

2. (20pts) In industrial selling, negotiation costs represent a significant percentage of a firm’s sales since the seller must formulate a sales strategy before negotiating with a business or governmental client. Several researchers Interviewed 500 firms involved in industrial selling and found their average negotiation cost per transaction to be $11,336 with a standard deviation of $1,951. What is the point estimate of the average negotiation cost per transaction for all industrial sellers? What are the lower and upper limits of a 90% confidence interval?

Answer 1

Solution:

Given that,

Sample size = n = 500

Sample mean = = 11336

Sample SD =  s = 1951

1)

What is the point estimate of the average negotiation cost per transaction for all industrial sellers?

Sample mean is the point estimate of the population mean

So ,

$11,336

2)

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 90% confidence interval.   

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 500 - 1 = 499

    =    =  _0.05,499  = 1.648

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * (s / n)

=  1.648 * (1951 / 500)

= 143.79026185

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(11336 - 143.79026185)   <   <  (11336 + 143.79026185)

11192.2097382 <   <  11479.7902619

Required 90% confidence interval is (11192.2097382 , 11479.7902619)