Question

A machine at Juice Fresh is set to fill fruit juice in 250ml cartons. It is known that when the machine is working properly, the mean amount of juice-filled is 250ml. A supervisor from the quality control department took a random sample of cartons and found that the mean amount of juice-filled was 258ml with a standard deviation of 16ml. Using the 1% significance level, the supervisor wants to test if the machine is working properly. Assume that the amounts of juice-filled in all such cartons follow the normal distribution.



Find the rejection region(s) and calculate the test statistics.
Hence, can you conclude that the mean amount of fruit juice filled is different from 250ml? Does the machine need adjustment?

Answer 1

Let the sample size n=25.

Critical t-value: t(0.005,24)=2.797.

Rejection region: t>2.797 or t<-2.797.

Test statistic: $t=\frac{258-250}{\frac{16}{\sqrt{25}}}=2.5.$

Since the t-value is less than the critical t-value, fail to reject the null hypothesis.

There is no sufficient evidence that the mean amount of fruit juice filled is different from 250ml.

The machine does not need adjustment.