You have taken a random sample of size n=85 from a normal population that has a population mean of μ = 120 and a population standard deviation of a = 19.Your sample, which is Sample 1 in the table below, has a mean of x = 121.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)(a) Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidenceinterval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)S4S5S6S7S1 121.8S2S3S8S9$10S11S12S13S14$15S16S17S18• Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.• For the points (and), enter the population mean, μ = 120.S19111.0S20111.0x75% confidence interval120.5XGenerate Samples130.0130.0Ś(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n=85 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.75% 75% 95% 95%lower upper lower upperlimit limit limit limit????111.0H+H|+++111.0111.075% confidence intervals95% confidence interval+||||||||120.5H+++130.0 111.0XH+H.130.095% confidence intervals5130.0|||||||||||130.0 19(c) Notice that for =95% of the samples, the 95% confidence interval contains the population mean. Choose the20correct statement.When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible thatmore or fewer than 95% of the samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% ofthe samples will contain the population mean.(d) Choose ALL that are true.If there were a Sample 21 of size n=170 taken from the same population as Sample 10, then the 95% confidenceinterval for Sample 21 would be narrower than the 95% confidence interval for Sample 10.The 75% confidence interval for Sample 10 is narrower than the 95% confidence interval for Sample 10. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.The 95% confidence interval for Sample 10 does not indicate that 95% of the Sample 10 data values are between115.3 and 123.3.From the 75% confidence interval for Sample 10, we know that there is a 75% probability that the populationmean is between 116.9 and 121.7.None of the choices above are true.

Question

You have taken a random sample of size n=85 from a normal population that has a population mean of μ = 120 and a population standard deviation of a = 19.Your sample, which is Sample 1 in the table below, has a mean of x = 121.8. (In the table, Sample 1 is written &#34;S1&#34;, Sample 2 is written &#34;S2&#34;, etc.)(a) Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidenceinterval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)S4S5S6S7S1 121.8S2S3S8S9$10S11S12S13S14$15S16S17S18• Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.• For the points (and), enter the population mean, μ = 120.S19111.0S20111.0x75% confidence interval120.5XGenerate Samples130.0130.0Ś(b) Press the &#34;Generate Samples&#34; button below to simulate taking 19 more samples of size n=85 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.75% 75% 95% 95%lower upper lower upperlimit limit limit limit????111.0H+H|+++111.0111.075% confidence intervals95% confidence interval+||||||||120.5H+++130.0 111.0XH+H.130.095% confidence intervals5130.0|||||||||||130.0 19(c) Notice that for =95% of the samples, the 95% confidence interval contains the population mean. Choose the20correct statement.When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible thatmore or fewer than 95% of the samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% ofthe samples will contain the population mean.(d) Choose ALL that are true.If there were a Sample 21 of size n=170 taken from the same population as Sample 10, then the 95% confidenceinterval for Sample 21 would be narrower than the 95% confidence interval for Sample 10.The 75% confidence interval for Sample 10 is narrower than the 95% confidence interval for Sample 10. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.The 95% confidence interval for Sample 10 does not indicate that 95% of the Sample 10 data values are between115.3 and 123.3.From the 75% confidence interval for Sample 10, we know that there is a 75% probability that the populationmean is between 116.9 and 121.7.None of the choices above are true.

Accepted Answer

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