A thermocouple probe is used to make temperature measurements of compressed air

Question

A thermocouple probe is used to make temperature measurements of compressed air tank. Twenty-five measurements of the temperature result in a mean value of 370 K with a sample standard deviation of 2.21 °C. Assuming negligible systematic errors, within what region around the mean value should contain true tank air temperature with 95% level of confidence? If one of the readings was 374.1 K, within what region around the one reading should contain the true air temperature with 99% level of confidence?

Explanation / Answer

Here we find the critical region are as below

Here xbar=370

Standard deviation =2.21

n=25

E=standard errror=zc×s/sqrt(n)

For 95% interval is zc is 1.96

=1.96×2.21/sqrt(25)

=1.96×2.21/5

=0.86632

The critical region is

(Xbar-E<mu<xbar+E)

(370-0.866,370+0.866)

(369.134,370.866)

This is the region around the mean value shoud contain above value

E=standard errror=zc×s/sqrt(n)

For 99% interval is zc is 2.58

=2.58×2.21/sqrt(25)

=2.58×2.21/5

=1.1403

The critical region is

(Xbar-E<mu<xbar+E)

(370-1.140,370+1.140)

(368.86,371.140)

This is the region around the mean value shoud contain above value

Here in the above two values we can see that the

374.1 is not belong to 99% level of confidennce

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