Sam is planning to open a dockless scooter company in Fayetteville and wants to estimate the amount of time a typical user would rent one. She visits a similar college town to investigate, where she randomly samples 20 customers and asks each to report the number of minutes the scooter was used. The average rental time was 142.21 minutes. Sam knows from national data that scooter rental time is a normally distributed variable with a standard deviation of 26.09 minutes. What would happen to the confidence interval if Sam sampled an additional 100 customers to the sample? a. It would probably not change b. It would get wider c. Sample size does not impact the width of the confidence interval d. It would become narrower

Respuesta :

Answer:

d. It would become narrower

Step-by-step explanation:

The width of a normal confidence interval is given by:

[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is the critical value according to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

W and n are inverse proportional, that is, as n(the sample size) increases, W(the width of the interval) decreases, that is, the interval becomes narrower..

So the correct answer is:

d. It would become narrower