Twenty measurements of the pressure of air in a tank are reported in the table.

Question

Twenty measurements of the pressure of air in a tank are reported in the table. Neglecting systematic errors, what is the best estimate of the tank pressure with 95% level of confidence? What is the best estimate if the level of confidence is increased to 99%?

Measurements of Tank Pressure (in kPa) 272.67 275.23 280.22 274.36 279.57 271 .00 278.95 279.85 273.69 269.96 282.62 278.57 274.04 268.07 79.29 1276.47 270.58 70948 30605 a51340 P77777 k22222 S27577 25-854 P09-986 87777 22222 ts 36529 3-6 23962 54829 7-7-7-8-7 22222 70967 64290 21298 77766 22222

Explanation / Answer

Solution:

Here, we have to find the best estimate or 95% and 99% confidence intervals for the tank pressure.

Confidence interval formula is given as below:

Confidence interval = Xbar -/+ t*SD/sqrt(n)

First of all we have to find the 95% confidence interval.

For the given data we have

Sample mean = Xbar = 275.21

Sample standard deviation = SD = 4.076141106

Sample size = n = 20

Confidence level = 95%

Degrees of freedom = n - 1 = 20 – 1 = 19

Critical t value = 2.0930

Confidence interval = 275.21 -/+ 2.093*4.076141106/sqrt(20)

Confidence interval = 275.21 -/+ 1.9077

Lower limit = 275.21 – 1.9077 = 273.30

Upper limit = 275.21 + 1.9077 = 277.12

Best estimate or confidence interval = (273.30, 277.12)

Now, we have to find the confidence interval for 99% confidence level.

For 99% confidence level, critical t value = 2.8609

Confidence interval = 275.21 -/+ 2.8609*4.076141106/sqrt(20)

Lower limit = 275.21 – 2.6076 = 272.60

Upper limit = 275.21 + 2.6076 = 277.82

Best estimate or confidence interval = (272.60, 277.82)

[Best point estimate is the sample mean 275.21]

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