A university is comparing the hourly wages of students of their university who c
ID: 3322278 • Letter: A
Question
A university is comparing the hourly wages of students of their university who completed a Master's Degree to students who only completed a Bachelor's Degree. Of the students surveyed, 56 had a Master's degree and 70 had a Bachelor's Degree only. The average hourly rate for those with a Master's was $41.138 (SD = $4.439). Among the graduates with a Bachelor's degree, the average hourly rate was $26.424 (SD = $8.435). You use this information to calculate a 99% confidence interval for the difference in mean hourly wage of (11.454, 17.974). Of the following statements, what is the best interpretation of this interval? We are 99% sure that the difference in average hourly wage of all nationwide graduates with a Master's degree and all nationwide graduates with a Bachelor's degree is between 11.454 and 17.974. 2) We do not know the population means so we do not have enough information to make an interpretation 3) We are 99% confident that the difference between the average hourly wage of all their graduates with a Master's degree and all their graduates with a Bachelor's degree is between 11.454 and 17.974. We are 99% confident that the difference between the average hourly wage of all their graduates with a Master's degree and all their graduates with a Bachelor's degree surveyed is between 11.454 and 17.974. 4) 05 We are certain that the difference between the average hourly wage of all graduates with a Master's degree and all graduates with a Bachelor's degree is between 11.454 and 17.974. SaveExplanation / Answer
As we have computed here the 99% confidence interval for the difference in the means, the interpretation of this is that there is a 0.99 probability that the difference in means for the population groups lies in the given confidence interval. ( not just the people surveyed. ) Therefore 4) is not correct here. Also we are not certain as the probability is 0.99 for the difference to lie in the confidence interval, therefore 5) is also not correct here.
3) is the correct answer here, as we are 99% confident that the mean of all the population groups mean would lie in the given interval.
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