The data set of the diameters of the metal cylinders manufactured an automatic machine has sample size of n=29, mean of x = 49.98 mm and std. of S = 0.14 mm. Expected diameter of metal cylinder is μ = 50.00 mm Can we be 95% confident that machine calibrated properly?

we say for μ = 50.00 mm we be 95% confident that machine calibrated properly with (49.926757, 50.033243)

Step-by-step explanation:

Given data

n=29

mean of x = 49.98 mm

S = 0.14 mm

μ = 50.00 mm

Cl = 95%

to find out

Can we be 95% confident that machine calibrated properly

solution

we know from t table

t at 95% and n - 1 = 29-1 = 28 is 2.048

so now

Now for 95% CI for mean is

(x - 2.048 * S/√n, x + 2.048 * S/√n)

(49.98 - 2.048 * 0.14/√29, 49.98 + 2.048 * 0.14/√29)

(49.926757, 50.033243)

hence we say for μ = 50.00 mm we be 95% confident that machine calibrated properly with (49.926757, 50.033243)