Q1: Descriptive statistics and two-group comparisons (25 marks)You are a software product development manager. Just before the start of a new project, yourteam installed and trained on a new design...

Q1: Descriptive statistics and two-group comparisons (25 marks)You are a software product development manager. Just before the start of a new project, yourteam installed and trained on a new design tool. On previous projects, the designers on your teamwere coding an average of 50 lines per day. Wanting to know if the new design tool is making adifference in productivity, you sample a day of coding output from 12 of your designers. Thenumber of lines coded by the developers in your sample were 67, 62, 46, 45, 54, 44, 52, 80, 60,48, 40, and 53.tendency and measures of variation. For each statistic, compute the result in two ways: i) afunction call from the R command line, and ii) using the formulas or techniques from the coursenotes. Briefly explain the meaning of each statistic.b) Test to see if the new design tool has made a difference in the average coding productivity ofthe designers on your team by computing a 95% confidence interval of the new population mean(lines of code produced using the new design tool), and comparing that result to the originalpopulation mean (lines of code produced without using the new design tool). The steps tocompute the confidence interval are as follows:i) Decide which of the two methods from the course notes for estimating confidence intervals ismost appropriate here (i.e., z-statistics or t-statistics). Explain the rationale for your choice.ii) Assess the normality of the data using the various methods from the course notes (i.e., thecentral limit theorem, q-q plots, and computing the “rule of thumb” skewness and kurtosis tests).Explain why this step is important.iii) Manually compute the 95% confidence interval of the new population mean using themethods from the TTMG 5004 class notes. Do this by plugging numbers into equations, lookingup values on tables of probability distributions, and showing all of your work. You are welcometo use R as a calculator to compute sums and other expressions but please do not use higher levelfunction calls or the R Commander GUI for this part of the assignment.iv) Interpret your results. Has the new design tool made a difference? What can we conclude?c) Perform a second test of whether the design tool has made a difference by computing a nullhypothesis statistical test (NHST) to compare the group means. The steps are as follows:i) Decide whether a one-tail or two-tail test is more appropriate here. Explain the rationale foryour choice.ii) Compute the result using either an R function call (e.g., the R “t.test” function) or RCommander (e.g., R Cmdr: Statistics/Means/Single-sample t-test...). Set a = 0.05.iii) Interpret your results. Has the new design tool made a difference? What can we conclude?