The sampling distribution of sample mean for a large population is approximately normal if the sample size is ans. 2 10 100 5

The sampling distribution of sample mean for a large population is approximately normal if the sample size is ans. 2 10 100 5

states that the sampling distribution of x is approximately normal when the sample is large.

A normal population has mean 100 and variance 25.How large must the random sample be if you want the standard error of the sample average to be 1.5?a.9b.10c.11d.None of the otherse.12

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of =σ23. We have taken a random sample of size =n95 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 =x140.9. Also shown are the lower and upper limits of the 80% 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 =μ140, which is shown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size =n95 from this same population. (The 80% 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.x 80%lowerlimit 80%upperlimit 95%lowerlimit 95%upperlimitS1 140.9 138.2 143.6 136.3 145.5S2 139.9 137.2 142.6 135.3 144.5S3 141.2 138.5 143.9 136.6 145.8S4 139.7 137.0 142.4 135.1 144.3S5 143.6 140.9 146.3 139.0 148.2S6 141.5 138.8 144.2 136.9 146.1S7 139.0 136.3 141.7 134.4 143.6S8 136.5 133.8 139.2 131.9 141.1S9 141.8 139.1 144.5 137.2 146.4S10 141.2 138.5 143.9 136.6 145.8S11 145.2 142.5 147.9 140.6 149.8S12 141.5 138.8 144.2 136.9 146.1S13 136.4 133.7 139.1 131.8 141.0S14 142.0 139.3 144.7 137.4 146.6S15 140.2 137.5 142.9 135.6 144.8S16 143.6 140.9 146.3 139.0 148.2S17 138.5 135.8 141.2 133.9 143.1S18 134.7 132.0 137.4 130.1 139.3S19 139.6 136.9 142.3 135.0 144.2S20 141.7 139.0 144.4 137.1 146.380% confidence intervals130.0150.095% confidence intervals130.0150.0(a)How many of the 80% confidence intervals constructed from the 20 samples contain the population mean, =μ140? (b)How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, =μ140? (c)Choose ALL that are true. The center of the 80% confidence interval for Sample 1 is 140.9, because the center of a confidence interval for the population mean must be the sample mean. For each sample, the 80% confidence interval for the sample is included in the 95% confidence interval for the sample. Since Sample 19 and Sample 20 are drawn from the same population, the center of the 95% confidence interval for Sample 19 must be the same as the center of the 95% confidence interval for Sample 20. All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there must have been errors due to rounding. None of the choices above are true.

Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.