Question

A manufacturer is trying to determine if a new chemical it is using changes the mean hourly yield of its production process. Historically, the mean level of production was a yield of 3 kg per hour. A sample of 16 hours of production finds a mean of 2.77 kg per hour and a standard deviation, s, of 0.3 kg per hour.

a) At the α=0.01 level of significance, test whether or not the new chemical has changed the mean hourly yield of the production process.

b) In the context of this situation, describe (for a layman) what making a Type I error or making a Type II error would mean.

Answer 1

a)

Null and alternative hypothesis:

Critical value:

At = 0.01 and df= 15, critical value, = 2.947

Test statistic:

Conclusion:

As |t| = 3.067 > 2.947, reject the null hypothesis.

b) Type I error : in this context type I error would be reject null hypothesis when it is true. means when the new chemical has not changed the mean but we conclude that it has.

Type II error: in this context type II error would be failing to reject null hypothesis when it is false. means when the new chemical has changed the mean but we conclude that it has not.