# PROBABILITY AND STATISTICS HOMEWORK

1. [22 points]Lack of sleep costs companies in lost productivity. A major airline recently began encouraging reservation agents to nap during their breaks. In a random sample of 10 of their reservation agents, when comparing the number of complaints about each during the 6 months prior to the policy change to the initial 6 months after, the mean number of complaints received fell by 3.9, with a standard deviation 4.306326.

(a) [5 points] Create hypotheses appropriate for the following research question: do the data present sufficient evidence to conclude the new napping policy reduced the mean number of complaints about reservation agents?

(b) [6 points] Check the conditions required to complete this test. Given the small sample size, the following boxplot, histogram (with overlaid normal curve) and normal probability plot for the ten observed differences have been provided for reference. Note: see section 1.6.5 on pp. 35-37 and 3.2 on pp. 137-141 for more information on identifying potential outliers and evaluating the normal approximation.

(c) [6 points] The test statistic and p-value for this test follow in the edited RStudio output below. What do you conclude? State your decision and conclusion in the context of the study. Follow the format of Problem 3, part (d) in Lab 2.

T <- (3.9-0)/(4.306326/sqrt(10)); T

[1] 2.863899

pt(q=T, df=9, lower.tail=F)

[1] 0.00933069

(d) [5 points] What type of error might we have made? Explain what the error means in this context.