Question

mu = 90, sigma = 1.5

how large should the sample size be, to detect a shift in mu to 91?

Answer 1

Answer)

Margin of error = 91 - 90 = 1

Given population s.d = 1.5

As the population s.d is known here we can use z table to estimate the sample size

Here you forgot to mention confidence level

So i will solve for three confidence levels then you can match with your mentioned confidence level

For 90% confidence level (0.90)

Critical value z from z table is 1.645

Margin of error = z*s.d/√n

1 = 1.645*1.5/√n

N = 7

For 95% confidence level (0.95)

Critical value is 1.96

1 = 1.96*1.5/√n

N = 9

For 99% confidence level (0.99)

Critical value is 2.58

N = 15