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°. Assume that the distribution of the actual temperatures for this model when the dial is set to 300° is Normal. To test if the dial is properly calibrated, we will test the following hypotheses: H0 : µ = 300 versus Ha : µ , 300.

(a) Based on the data, what is the value of the one-sample t statistic?

(b) Are the data statistically significant at the 5% significance level?

i. Yes, because the P-value is less than 0.05.

ii. Yes, because the sample mean x¯ = 305°, which is much higher than 300°.

iii. No, because a difference of 5° (between x¯ and µ) as compared to 300° is very small (insignificant).

iv. No, because the P-value is greater than 0.05.

Answer 1

H0: mu = 300
Ha: mu not equals 300

a)
xbar = 305
s = 4.0825
n = 4

test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (305 - 300)/(4.0825/sqrt(4))
t = 2.45

b)
p-value = 0.0917

No, because the P-value is greater than 0.05.