Prove that average reduces Variance

A least squares line for a sample with 11 observations has an SSE = 192; calculate and s. Please show your work So i can understand how you arrived at the answer

A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 13.2 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance?   Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?   (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal…

Which one of the following assumptions is required for the 2SLS estimator to be consistent? a) There are perfect linear relationships among the instrumental variables b) There is a correlation between each instrumental variable and the endogenous variable c) The conditional variance of the error term depends on an exogenous explanatory variable d) There is a strong correlation between each instrumental variable and the error term

A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 20 batteries gave a sample variance of 13.8 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance?State the null and alternate hypotheses. A. Ho: σ2 = 23; H1: σ2 ≠ 23 B. Ho: σ2 = 23; H1: σ2 < 23     C. Ho: σ2 = 23; H1: σ2 > 23 D. Ho: σ2 > 23; H1: σ2 = 23 (b) Find the value of the chi-square statistic for the sample. (Round…

If I was calculating the variance of this list of numbers (attached), do I need to include the "no home games" as a 0 and base the calculation on 14 entries?  Or do I just leave them out completely and base the calculation on 12 entries?

Identify which of the following scatterplots contain possible outliers or observations influential for the least squares regression line. Select all that apply 100- 90- 80- 을 70어 3 60- 50- 40- 25 20- 20 15 - 10- 5 10 15 20 25 30 35 40 45 50 20,000 40,000 60,000 80,000 100,000 120,000 Number of incorrect answers Distance driven (mi) Age (years) Outlier Influential observation Outlier 70 24– 50- 65 60 - 22- 40- 55 - 20-. 8 30- 50 – 18- 20- 45 65 70 75 80 5.0 5.5 6.0 6.5 7.0 7.5 8.0 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 Daily high temperature (°F) Price of gasoline ($/gal) Hours slept Influential observation No outliers or influential observations Outlier Answer Bank Influential observation Outlier No outliers or influential observations Daily low temperature (°F) Duration of commute (min) Years of full-time employment Number of oil changes (zo) pəwnsuoɔ əəyoɔ

Which of the following is the research hypothesis of one-tailed dependent t-test expecting to see a significant decrease in the observed scores?          A. mean(posttest) < mean(pretest)         B. mean(posttest) = mean(pretest)         C. mean(posttest) > mean(pretest)     D. mean(posttest) ≠ mean(pretest)