Suppose we have two groups of students, those who go for tutoring help and those who do not. The following is the mathematics test results from these two groups of students. with tutor help without tutor help 75 66 80 82 73 64 51 58 93 81 67 65 76 59 88 47 52 60 (a) Test for the equality of variances of mathematics test results from the students with and without tutoring help at a = 0.1 (b) Test whether there is difference in the mean mathematics test results for the students with and without tutoring help at 2% significance level. (c) Find the 95% confidence interval for the difference between two groups' average mathematics test results.

Imagine that you were hired as a consultant by a local business owner tohelp her determine how many paid days off she should provide to her employees. In general, she wants to establish some sort of standard for her employees and for herself. Based on data provided by the government, you conclude that on average, workers in the United States take 14 paid days off per year. The data for the eight employees who work at the company you are consulting for are: 12, 9, 7, 12, 13, 14, 14, and 12 days. Thequestion you are trying to answer is, are the number of days off taken by the eight employees statistically different from the data provided by the US government? (I have stated the null and alternative hypotheses, and found that this is a two-tailed test. With alpha=0.05, I have found the t-critical value to be +/- 2.365, with DF=7)I need help with:  A. Compute the appropriate test statistic. Use the computational formula tocompute the sample standard deviation. Show all formulas that you…

On the night our play-off was being held, a number of vehicles were in the east parking lot of the gym. Half of the white vehicles were neither cars nor buses. There were 8 buses in all, and only 1 of those was yellow. There were 16 other yellow vehicles, though, and 6 of those were cars. Of a total of 20 cars, 9 were not yellow or white. There were as many white buses as there were buses thatt were not white, Besides cars and buses, of course, there were vans and trucks. How many white vehicles were there Students, draw anywhere on this slide!

Rita has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Rita has recorded the travel times for samples of twelve trips via the 10 Freeway and twelve trips via the 60 Freeway. The following table gives the travel times (in minutes) for the twenty-four trips.   Travel times in minutes 10 Freeway 66, 70, 73, 71, 72, 71, 65, 74, 69, 71, 75, 71 60 Freeway 77, 72, 71, 68, 74, 80, 70, 78, 76, 71, 68, 67 Assume that the two populations of travel times are normally distributed and that the population variances are equal. Can we conclude, at the 0.01 level of significance, that the mean travel time via the 10 freeway, μ1, is different from μ2, the mean travel time via the 60 freeway? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and…