Question

The administrators at the University of Oklahoma wonder if Oklahoma residents or non-Oklahoma residents differ in their excitement to go home for the holidays following final exams. They randomly select 100 Oklahoma residents and 100 non-Oklahoma residents for their study. They then ask all participants to rate their excitement level on a scale of 1-10. The mean excitement level for Oklahoma residents was 7.745, while the mean excitement level for non-Oklahoma residents was 7. They create the following 95% confidence interval for the mean difference: -1.78 to 3.27. Which of the following is the best way to interpret their results based on their confidence interval?

a. The administrators are 95% confident that Oklahoma residents are significantly more excited than non-Oklahoma residents to go home for the holidays.
b. The administrators are 95% confident that Oklahoma residents are significantly less excited than non-Oklahoma residents to go home for the holidays.
c. The administrators are 95% confident that Oklahoma residents significantly differ from non-Oklahoma residents in their excitement to go home for the holidays because their interval covers 0.
d. The administrators are unable to tell if there is a true difference between Oklahoma and non-Oklahoma residents in their excitement to go home for the holidays because their interval covers 0.

Answer 1

The correct interpretation of the 95% confidence interval from -1.78 to 3.27 for the difference in excitement levels between Oklahoma and non-Oklahoma residents is that administrators cannot determine a true difference because the interval includes zero, meaning there could be no difference or differences both ways. So the correct option is d.

Step-by-step explanation:

When interpreting a 95% confidence interval for the mean difference in excitement levels between Oklahoma residents and non-Oklahoma residents regarding going home for the holidays, it is important to consider the interval range provided, which is from -1.78 to 3.27. Because the interval includes the value 0, it suggests that the difference in mean excitement levels could be non-existent. Therefore, the correct interpretation would be:

d. The administrators are unable to tell if there is a true difference between Oklahoma and non-Oklahoma residents in their excitement to go home for the holidays because their interval covers 0.

This implies that the confidence interval includes the possibility that there is no difference at all, as well as potential differences in both directions (Oklahoma residents being more or less excited than non-Oklahoma residents). The interval does not provide clear evidence to claim a significant difference in either direction with 95% confidence.

Answer 2

d. The administrators are unable to tell if there is a true difference between Oklahoma and non-Oklahoma residents in their excitement to go home for the holidays because their interval covers 0.

Step-by-step explanation:

The confidence interval refers to a rabje of statistically calculated values used in establishing a certain level of confidence in the outcome of a data.

The confidence interval is calculated thus :

Mean ± (Zcritical * Error)

The ± sign ensures we have the lower and upper boundary of our confidence level.

From the confidence level given in the question : -1.78 to 3.27

Since 0 is contained in the confidence interval range given, then it can be concluded that the difference in excitement between Oklahoma and non oklahoma residents cannot be adequately established.