Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in µF, was computed to be (0.213,0.241). Find a 90% confidence interval for the mean capacitance of this type of capacitor

Step 1 of 3:

Based on a large sample of capacitors of a certain type, the 95% CI for the mean capacitance is (0.213,0.241). We have to find the 90% CI for the mean capacitance of the same type of capacitor.

Step 2 of 3:

To find the 95% confidence interval for the mean capacitance,

set t = .95

1- t = 0.05

= 0.025

We have to find the Z-score , = .

We can find from the normal table (area under normal curve). The value 0.975 falls in the row 1.9 under column 0.06.

So the 95% CI for the mean capacitance is

If the population mean and variance is unknown then we can estimate the CI as

……. (1)

Similarly in order to find the 90% CI for the mean capacitance,

set t = .90

1- t = 0.1

= 0.05

We have to find the Z-score , = .

We can find from the normal table (area under normal curve). The value 0.95 falls in the row 1.6 under column 0.04.

So the 90% CI for the mean capacitance is

The estimate of the CI will be

…….. (2)