The desired amount of a chemical component X in a certain ty

The desired amount of a chemical component (X) in a certain type of aluminous cement is 5.5. To test whether the true average amount is 5.5 for a production facility, 16 independent samples are analyzed. Suppose that the amount of component X in a sample is normally distributed with = 0.3 and that the sample mean is = 5.25.

Solution

H0: mu = 5.5

Ha: mu is not equal to 5.5

X follows a normal distribution

Sample mean x bar = 5.5

Std dev = 0.3

std error of sample = 0.3/rt n = 0.075

Mean difference = 5.5-5.25 = 0.25

Test statistic = 0.25/0.075

= 3.333

df = 15

p value = .004541.

The result is significant at p < .05.

Hence reject null hypothesis that the sample mean = 5.25