A manufacturer of heaters wants to determine if the height of the heater warms a room more quickly.Four different heights were studied.The shortest heater group had n=12 with an average time to heat the room of 15.9 minutes.The tallest heater group had n=10 with an average time to heat the room of 17.3 minutes.Using an alpha of 0.01, MSE of 2.88, and N=44, would the research find evidence of a significant difference in these brands?
A)Yes, as the difference in the means is larger than the critical value
B)No, as the critical value is smaller than the overall sample size
C)Yes, as the difference in the means is smaller than the critical value
D)No, as the difference in the means is larger than the critical value
E)No, as the difference in the means is smaller than the critical value

Question

Quizplus · Accepted Answer

To determine if there's a significant difference between the groups, a t-test or similar statistical test comparing the means of the two groups would be used. The critical value in this context refers to the value that the test statistic must exceed for the difference to be considered statistically significant. The statement that the difference in the means is smaller than the critical value suggests that the observed difference between the average times to heat the room (15.9 minutes for the shortest heater group and 17.3 minutes for the tallest heater group) is not large enough to be statistically significant at the alpha level of 0.01, given the variability in the data (MSE of 2.88) and the sample sizes of the groups. This implies that the research would not find evidence of a significant difference in heating times between the different heights of heaters based on the provided data.

A Manufacturer of Heaters Wants to Determine If the Height