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. Assuming that the actual temperatures for all ovens of this model when the dial is set to 300°F are Normally distributed with mean ?, and standard deviation ? = 4°F, we test whether the dial is properly calibrated by testing the following hypotheses: H0: ? = 300, Ha: ? ? 300 If the null hypothesis is rejected for any sample average that is smaller than 295°F or for any sample average that is larger than 305°F, the power of our test when ? = 310°F is approximately: 0.006. 0.470. 0.994. 0.530.

Explanation / Answer

here for std error =std deviation/(n)1/2 =4/(4)1/2 =2

hence power of the test =P(Xbar<295)+P(Xbar>305)=P(Z<(295-310)/2)+P(Z>(305-310)/2)

=P(Z<-7.5)+P(Z>-2.5)=0+0.994 =0.994

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