Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard dev

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Suppose We Are Interested In Studying A Population To Estimate Its Mean The Population Is Normal And Has A Standard Dev 1 (38.59 KiB) Viewed 34 times

Suppose We Are Interested In Studying A Population To Estimate Its Mean The Population Is Normal And Has A Standard Dev 2 (30.85 KiB) Viewed 34 times

Suppose We Are Interested In Studying A Population To Estimate Its Mean The Population Is Normal And Has A Standard Dev 3 (30.14 KiB) Viewed 34 times

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of σ=5, We have taken a randam sample of size n=10 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", ete.) As shown in the table, the sample mean of Sample 1 is xˉ=100.3. Also shawn 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 90% confidence interval, Suppose that the true mean of the population is μ=100, which is: shown on the dispiays for the confidence intervals. Press the "Generate 5 amples" button to simulate taking 19 more rancom samples of size n=10 from this same population. (The 75% and 90% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ=1007 (b) How many of the 90% confidence intervals constructed from the 20 samples contain the popuiation mean, μ=1007$17 (c) Choose Aut that are true. For each sample, the 75% confldence interval for the sample is included in the 90% confldence interval for the sachple. The sample means for Samale 19 and Sample 20 are different, so the center of the 90% confidence interval for 5 ample t9 is different from the cemer of the 90% confidence interval for 5 ample 20 . We woud exeect to find mere 75%, contidence intervats, that contain the oooulation mean than 90 A confidence intervals.
(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ=100 ? (b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, μ=100? (c) Choose Al. that are true. For each sample, the 75% confidence interval for the sample is included in the 90% confidence interval for the samplec. The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval for 5 ample 19 ts dffferent from the center of the 90% confidence interval for Sample 20 . We would expect to find more 75% confidence intervals that contain the population mean than 90 . contidence intervals that contain the papulation mean. Given a sample, a higher confidence level results in a narrower interval. Tt is not surprising that some 75% contidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. Nione of the choices above are true.