Question

A random sample of 45 door-to-door salespersons were asked how long on average they were able to talk to the potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes. Which Excel statements will construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer.

a.
=8.5+1.96*9/SQRT(45), and =8.5-1.96*9/SQRT(45)

b.
=8.5+1.96*3/SQRT(45), and =8.5-1.96*3/SQRT(45)

c.
=45+1.96*3/SQRT(9), and =45-1.96*3/SQRT(9)

d.
=45+0.95*3/SQRT(9), and =45-0.95*3/SQRT(9)

e.
None of the above.

A random sample of 45 door-to-door salespersons were asked how long on average they were able to talk to the potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes. What is the point estimate for the average conversation length?

a.
45 salespersons

b.
9 minutes

c.
8.5 minutes

d.
5 minutes

e.
None of the above.

Answer 1

b. =8.5+1.96*3/SQRT(45), and =8.5-1.96*3/SQRT(45)

Explanation:

Sample size (n) = 45

Sample mean (M) = 8.5 minutes

Variance (V) = 9 minutes

Z-score for a 95% confidence interval (z) = 1.96

A confidence interval is defined by the following expression:

`M\pm z\sqrt{(V)/(n) }`

Applying the given data:

`8.5\pm 1.96\sqrt{(9)/(45) }\\8.5\pm 1.96(3)/(\sqrt 45)`

Writing in Excel statements, the limits of the interval would be

=8.5+1.96*3/SQRT(45), and =8.5-1.96*3/SQRT(45)

Therefore, the answer is alternative b.