Business statistics

Question

If n=24, x¯(x-bar)=40, and s=8, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

_______ < μ < _______

Answer 1

Hi Salma,

Formula for normally distributed, two-sided confidence intervals is:

CI=x-bar +/- z*SE

Breaking this down:

x-bar=sample mean

z*=z-critical value

SE=standard error

Let's talk about standard error, since it has its own formula:

SE=s/sqrt(n)

s=standard deviation

n=sample size

For this problem:

s=8

n=24

SE=8/sqrt(24)

SE=1.633

Now, looking at z*, the z-critical value. 98% is a somewhat rare confidence level, but I've seen it more on Wyzant than anywhere else, so it may be worth committing this z* to memory or writing on formulas sheet if allowed.

z*_0.98=2.326

Now, returning to our original formula:

CI=x-bar +/- z*SE

x-bar=40

z*=2.326

SE=1.633

CI=40 +/- (2.326*1.633)

CI=(36.202, 43.798)

Reducing to one decimal place and putting in requested notation:

36.2 < mu < 43.8

I hope this helps.