From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa. If more measurements are taken, estimate the expected range of pressure for 95% of the measurements.

Answer: (4.95, 4.99)

Explanation: This question simply wants us to construct a 95% confidence level for the population mean of pressure controller.

n = sample size = 19

x = sample mean = 4.97

s = sample standard deviation = 0.0461

To construct a confidence interval for mean, we need a critical value for a two tailed test, for this question we will make use of a t tail test to get our critical value because sample standard deviation is given and sample size is less than 30 (19).

At 95% confidence interval, it implies that our level of significance (α) is 5%.

The 95% confidence interval for mean is given below as

Upper limit

u = x + tα/2 * (s/√n)

Lower limit

u = x - tα/2 * (s/√n)

The value of tα/2 is gotten using a t test table and from the table, we have tα/2 as 2.10092

By substituting the parameters, we have that

For upper limit

u = 4.97 + 2.10092 * 0.0461/√19

u = 4.97 + (2.10092 * 0.0106)

u = 4.97 + 0.0222

u = 4.99

For lower limit

u = 4.97 - 2.10092 * 0.0461/√19

u = 4.97 - (2.10092 * 0.0106)

u = 4.97 - 0.0222

u = 4.95

Confidence interval = (4.95, 4.99)