A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% confidence interval for the mean yield when the new catalyst is used.

Answer:

Step 1 of 1:

In this question, we are asked to find a 99% confidence interval for the mean yield when the new catalyst is used.

The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%.

The yields are independent and approximately normally distributed.

When the sample size is small, and the population is approximately normal, we can use the Student’s t distribution to compute confidence intervals.

Let be a small random sample from a normal population with mean . then a level confidence interval for is

……….(1)

Where is a Student’s distribution with degrees of freedom, is sample mean, is a sample standard deviation and is a number of samples.

Hence , and .

For a 99% confidence interval, the value of is,

and

Putting the value into equation (1)

The value of = 3.250 from t table, hence our equation become,

0.725

Hence a 99% confidence interval for the mean yield when the new catalyst is used is (0.7846, 0.6654).