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.
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.
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