The 4-day work week is growing in popularity, with some large-scale studies currently underway. In the UK, for instance, several dozen companies have agreed to undergo a 6-month trial during the second half of 2022. Suppose that one such office manager takes part in the trial and will base her decision on 4-day vs. 5-day weeks purely on which option leads to the highest average employee productivity. The office manager takes a random sample of 78 employees. Prior to the start of each week, she randomly assigns the employees to either a 4-day week or a 5-day week. At the end of the week, she records their productivity. She does this over a period of 6 months, with every employee working 12 weeks on a 4-day schedule and 12 weeks on a 5-day schedule. (a) Which type of test should the office manager use to determine whether there is a difference in average productivity for 4-day weeks vs 5-day weeks?

one proportion z-testtwo sample t-test one sample t-testt-test for paired data

(b) The office manager computes the p-value = 0.03. What can be said about the difference in productivity, for = 0.05?

The observed difference in productivity is greater than you would expect from random sampling variation.The observed difference in productivity is likely to be nothing other than random sampling variation.

(c) Given the p-value = 0.03, what can be said about the corresponding 95% confidence interval for the difference in productivity scores?

0 is inside the 95% confidence interval.0 is outside the 95% confidence interval.

(d) Does this study design allow the office manager to determine the observed difference in productivity is caused by 4-day vs. 5-day weeks?

No, this an observational study which doesn't address causation.Yes, the study design makes it possible to determine causation.