We wish to see if the electronic control indicating the oven temperature for a certain model oven is properly calibrated.Four ovens of this model are selected at random.The electronic control on each is set to 300°F;after 1 hour,the actual temperature of each is measured.The temperatures measured are 305°F,310°F,300°F,and 305°F.Assume that the distribution of the actual temperatures for this model when the electronic control is set to 300°F is Normal.To test if the electronic control is properly calibrated,we will test the following hypotheses: H₀: $\mu$ = 300 versus H_a: $\mu$$\neq$300.Are the data statistically significant at the 5% significance level? A)Yes,because the P-value is less than 0.05. B)Yes,because the sample mean = 305°F,which is much higher than 300°F. C)No,because a difference of 5°F (between and $\mu$)as compared with 300°F is very small (insignificant). D)No,because the P-value is greater than 0.05.

Question

Quizplus · Accepted Answer

To test the hypotheses, we need to calculate the sample mean and the standard deviation of the sample. The sample mean is (305 + 310 + 300 + 305)/4 = 305°F. The sample standard deviation can be calculated using the formula:

s = sqrt[ ( (305-305)^2 + (310-305)^2 + (300-305)^2 + (305-305)^2 ) / (4-1) ] = 4.27°F

We can then calculate the test statistic:

t = (305 - 300)/(4.27/sqrt(4)) = 1.17

Using a t-distribution with 3 degrees of freedom (since n-1=3), and a significance level of 5%, the critical value is 3.182.

Since 1.17 is less than 3.182, we fail to reject the null hypothesis. Therefore, the data is not statistically significant at the 5% significance level. The correct choice is D.

We Wish to See If the Electronic Control Indicating the Oven