Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction. a sample of 12 batches was prepared using catalyst 1, and a sample of 10 batches was prepared using catalyst 2. the 12 batches for which catalyst 1 was used in the reaction gave an average yield of 85 with a sample standard deviation of 4, and the 10 batches for which catalyst 2 was used gave an average yield of 81 and a sample standard deviation of 5. find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances.

2.083 < µ1 - µ2 < 5.917  

Step-by-step explanation:

We will need to construct a 90% confidence interval for the difference of 2 means where the populations are normally distributed, and their variances are equal.

The calculations of the sample means and standard deviations are done for us.

Sample 1: Catalyst 1

n = 12, x = 85, s = 4

Sample 2:  Catalyst 2

n = 10, x = 81, s = 5

See attached photo for the construction of the confidence interval...

Step-by-step explanation:

This is how you would proceed:

Centered at D, draw an arc of 7m (3.5cm) within the garden (rectangle).

Centered at B, draw an arc of 4m (2cm) within the garden.

There will be two intersection points, one is outside the garden (that you will not see), and the other is within the garden, which is where the tree should be planted.

See illustration attached.