Two populations are surveyed using simple random samples. A sample of size n1 is used for population I, which has a population standard deviation of σ 1, and a sample of size n2 = 2n1 is used for population II, which has a population standard deviation σ 2 = 2 σ 1. For which of the two samples would you expect the sample mean to be more accurate?

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of σ = 16. We have taken a random sample of size n = 80 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is x=58.9. Also shown are the lower and upper limits of the 75% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is μ=60, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 80 from this same population. (The 75% and 95% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table. 75% x 75% 95% 95% lower upper lower upper limit…

You have a population mean µ=27, and a sample mean of 29. The sample variance equals 6. Compute Cohen’s d

A variable of two populations has a mean of 30 and a standard deviation of 18 for one of the populations and a mean of 30 and a standard deviation of 32 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 16, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. OA. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x₁-x₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. B. No, the formulas for the mean and standard deviation of…