Question

You work for a company that is interested in estimating the average number of monthly complaints received at various retail locations. They have gathered data from n = 64 locations and found the sample mean to be x = 87.5 and they know from past studies that the base data is approximately normal with variance σ^2 = 16.

a) Construct a 95 % confidence interval for the population mean number of calls µ.

b) If you wanted to construct a 95% confidence interval for the population mean number of calls µ but also ensure the width of your confidence interval is at most 1, how many samples would you need to take? Answer: So we would need to take at least 246 samples to ensure a 95% confidence interval with a width of at most 1. (show work to get this answer)

c) construct a 95% upper confidence bound for µ.

d) construct a 95% lower confidence bound for µ.

Answer 1

Answer)

As the population s.d is known here we can use standard normal z table

N = 64

Mean = 87.5

S.d = √16 = 4

A)

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*S.D/√N = 1.96*4/√64 = 0.98

Upper bound = mean + moe = 87.5 + 0.98 = 88.48

Lower bound = mean - moe = 86.52

B)

Moe = 1

We need to find n

1 = 1.96*4/√n

N = 62