Question

A drug store chain provides an app to its customers to track their shopping habits. One statistic the app

tracks is the amount of money the customer saves by purchasing sale items. The company's sales

team pulls data from the previous year for a random sample of 50 customers. They find that the

mean amount of money saved by these customers in the previous year is $154 with a standard

deviation of $26.

(a) Construct a 99% confidence interval for the true mean amount of money saved by all customers

in the previous year by purchasing sale items.

(b) The sales team would like to repeat this study with the goal of obtaining a smaller margin of

error. Propose two changes that would decrease the margin of error. What are potential

drawbacks if those changes are implemented?

Answer 1

a) CI ( 99% ) = ( 145,45 : 162,55)

b) b) In order to decrease the MOE the sales team has to increase the sample or decrease de 99% of the CI let´s say to 95 % but in that case

you will increase de error type I

Explanation:

a) CI = 99 % α = 1% α = 0,01

From z-table z(c) ≈ - 2,325 |z(c)| ≈ 2,325

CI = ( μ₀ ± z(c) * σ/√n )

CI = ( 154 - (2,325) * 26/√50 ; 154 + (2,325) * 26/√50 )

CI = ( 154 - 8,55 ; 154 + 8,55

CI ( 99% ) = ( 145,45 : 162,55)

b) In order to decrease the MOE the sales team has to increase the sample or decrease de 99% of the CI let´s say to 95 % but in that case

you will increase de error type I