Question

An engineer who is studying the tensile strength of a steel alloy knows that tensile strength is approximately normally distributed with σ = 60 psi. A random sample of 12 specimens has a mean tensile strength of 3450 psi.

a) How would the confidence interval change if we did not know that σ = 60 psi, but the number of specimens is 80?

b) How would the confidence interval change if we did not know that σ = 60 psi, but the number of specimens is 10?

Answer 1

a)

Now the population standard deviation is unknown so we need to use t critical value instead of z critical value. Sample size is 80 which is large so t critical value will be approximately same z critical value. That is confidence interval will not chnage. It will approximatey same as before.

b)

Sample size is 10 which is small but t critical value can be used becuase population is normally distributed. But t criitical value will be diffeent from z critical value. That is confidence interval will chnage. Generally sample standard deviation is larger than population standard deviation and t critical value is also larger so confidence intervall will be wider.