The variance statistic is an unbiased estimator of the population variance.

How is it that estimates of variance can be used to test a hypothesis about means?

A one-way Analysis of Variance (ANOVA) was used to examine whether students’ scores on a standardized test is a function of the teaching method they received (either lecture only, hands-on learning only, or both together). The ANOVA was significant. Run post hoc tests (by hand!) to determine which pairs of the mean are significantly different. Do the math for each and then explain in what way are they different. Method N Mean SD   Source df SS MS F Lecture Only 15 82.8 9.59   Between 2 736.53 368.27 5.34 Hands-On Only 15 88.53 8.73   Within 42 2895.47 68.94   Both 15 92.67 6.22   Total 44 3632     Total 45 88

A manager believes that the variance of output on the second shift is greater than the variance on the day shift. The following data are collected:   50 samples on the day shift; variance = 500 40 samples on the second shift; variance = 900 Set up hypotheses Perform a test and state your conclusions.

true or false MSBetween represents the variability that is only affected by unsystematic factors.

Construct a numerical example, i.e., a data set, such that a two-sample t-test will yield an insignificant test result but a pair t-test will yield a significant test result. (For the two-sample t-test, you can either assume equal variances or unequal variances, which will not affect the key idea of this question.) I need to know how this is possible and what the basics of making this data set should be.

When using an Analysis of Variance test, in order to find out which specific means are different from one another which test is used? a. t-test b. post hoc test c. Cohen’s D test d. Chi-square test

The variance in a production process is an importance measure of the quality of the process. A large variance often signals an opprotunity for improvement in the process by finding ways to reduce the process variance. The conduct a statistical test to determine whether there is a significant differeence between the variance in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?    Machine 1 Machine 2 2.95 3.22 3.45 3.30 3.50 3.34 3.75 3.28 3.48 3.29 3.26 3.25 3.33 3.30 3.20 3.27 3.16 3.38 3.20 3.34 3.22 3.35 3.38 3.19 3.90 3.35 3.36 3.05 3.25 3.36 3.28 3.28 3.20 3.30 3.22 3.28 2.98 3.30 3.45 3.20 3.70 3.16 3.34 3.33 3.18   3.35   3.12   Please use excel

Actuaries use various parameters when evaluating the cost of a life insurance policy. The variance of the life spans of a population is one of the parameters used for the evaluation. Each year, the actuaries at a particular insurance company randomly sample 30 people who died during the year (with the samples chosen independently from year to year) to see whether the variance of life spans has changed. The life span data from this year and from last year are summarized below. Current Last Year Year x1 = 75.8 | x,= 76.2 si= 47.61 s3= = 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the…

What correctly represents the coefficient of determination in terms of the variance that is an output from the analysis of variance table?