Question

To calibrate a thermometer, a technician tests it on water whose temperature is known to be 40◦F. She gets the following readings (all in degrees Fahrenheit): 49, 38, and 41. Based on this data, should she recalibrate the device?

Answer 1

Here we have to test the following hypothesis

In order to do so, we use the t-test for mean with n-1 degree of freedom, whose test statistics is given by

Here

So under null hypothesis H0 and using data, we get t=0.8128 with 3-1=2 df. To compair this with 5% critical value, we use the table of t-distribution, and obtain it as 4.3027. Notice that this value is greater than the calculated t value. So we can not accept the null hypothesis, that is true mean is not equal to 40 or she should recalibrate the device .