Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of = 11. We have taken arandom sample of size n = 15 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 = 112.8. Also shown are the lower and upper limits of the 75% confidence interval for the populationmean 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 = 115, which isshown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 15 from this same population. (The 75% and 90% confidenceintervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.75% 75% 90% 90%lower upper lower upperlimit limit limit limitS1 112.8 109.5 116.1 108.1 117.5S2 113.9 110.6 117.2 109.2 118.6S3 116.4 113.1 119.7 111.7 121.1S4 111.0 107.7 114.3 106.3 115.7S5 113.1 109.8 116.4 108.4 117.8S6 114.0 110.7 117.3 109.3 118.7S7 116.3 113.0 119.6 111.6 121.058 116.3 113.0 119.6 111.6 121.059 111.0 107.7 114.3 106.3 115.7S10|113.8|110.5 | 117.1 | 109.1 | 118.5511 1145|1112| 117.8 |1098|1192$12 119.0 115.7 122.3 114.3 123.7S13 113.6 110.3 116.9 108.9 118.3S14 119.1 115.8 122.4 114.4 123.8$15 109.9 106.6 113.2 105.2 114.6S16 116.6 113.3 119.9 111.9 121.3117.2 109.2 118.6S18 109.9 106.6 113.2 105.2 114.6S17 113.9 110.6S19 114.6 111.3 117.9 109.9 119.3$20 115.6 112.3 118.9 110.9 120.3H105.075% confidence intervalsH125.0 105.090% confidence intervalsEll+125.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 115?(b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, u = 115?(c) Choose ALL that are true.For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for othersamples, this is not the case.It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Eachconfidence interval depends on its sample, and different samples may give different confidence intervals.We would expect to find more 75% confidence intervals that contain the population mean than 90% confidenceintervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval forSample 19 is different from the center of the 90% confidence interval for Sample 20.None of the choices above are true.XŚ

Question

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of = 11. We have taken arandom sample of size n = 15 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written &#34;S1&#34;, Sample 2 is written &#34;S2&#34;, etc.)As shown in the table, the sample mean of Sample 1 is x = 112.8. Also shown are the lower and upper limits of the 75% confidence interval for the populationmean 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 = 115, which isshown on the displays for the confidence intervals.Press the &#34;Generate Samples&#34; button to simulate taking 19 more random samples of size n = 15 from this same population. (The 75% and 90% confidenceintervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.75% 75% 90% 90%lower upper lower upperlimit limit limit limitS1 112.8 109.5 116.1 108.1 117.5S2 113.9 110.6 117.2 109.2 118.6S3 116.4 113.1 119.7 111.7 121.1S4 111.0 107.7 114.3 106.3 115.7S5 113.1 109.8 116.4 108.4 117.8S6 114.0 110.7 117.3 109.3 118.7S7 116.3 113.0 119.6 111.6 121.058 116.3 113.0 119.6 111.6 121.059 111.0 107.7 114.3 106.3 115.7S10|113.8|110.5 | 117.1 | 109.1 | 118.5511 1145|1112| 117.8 |1098|1192$12 119.0 115.7 122.3 114.3 123.7S13 113.6 110.3 116.9 108.9 118.3S14 119.1 115.8 122.4 114.4 123.8$15 109.9 106.6 113.2 105.2 114.6S16 116.6 113.3 119.9 111.9 121.3117.2 109.2 118.6S18 109.9 106.6 113.2 105.2 114.6S17 113.9 110.6S19 114.6 111.3 117.9 109.9 119.3$20 115.6 112.3 118.9 110.9 120.3H105.075% confidence intervalsH125.0 105.090% confidence intervalsEll+125.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 115?(b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, u = 115?(c) Choose ALL that are true.For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for othersamples, this is not the case.It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Eachconfidence interval depends on its sample, and different samples may give different confidence intervals.We would expect to find more 75% confidence intervals that contain the population mean than 90% confidenceintervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval forSample 19 is different from the center of the 90% confidence interval for Sample 20.None of the choices above are true.XŚ

Accepted Answer

Confidence intervals computed from these 20 samples are

x¯
75% lower limit
75% upper limit…