We wish to see if the dial indicating the oven temperature for a certain model o

Question

We wish to see if the dial indicating the oven temperature for a certain model oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300°F, and, after one hour, the actual temperature of each is measured. The temperatures measured are 305°, 310°, 300°, and 305°. Assuming that the actual temperatures for this model when the dial is set for 300° are Normally distributed with mean , we test whether the dial is properly calibrated by testing the hypotheses H0 : = 0 versus Ha : 0 . Based on the data, the P-value for this test is

a. between 0.10 and 0.05.

b.between 0.05 and 0.025.

c.between 0.025 and 0.01.

Explanation / Answer

Sx = 4.0825
n = 4
x bar = 305

Sx / 2 = 2.0413

t = 305 - 300 / 2.0413 = 2.4494,

p-value you have to do 2tcdf (2,4494, 1000, 3).

You have to multiply by 2 because it is a 2 sided test,

we have 3 degrees of freedom because n = 4, and df = n-1.

The p-value is .0459, which is  between 0.10 and 0.05.

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