You have taken a random sample of size n = 19 from a normal population that has a population mean of μ = 50 and a population standard deviation of o=15.Your sample, which is Sample 1 in the table below, has a mean of x =45.3. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)(a) Based on Sample 1, graph the 75% and 90% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidenceinterval, and use 1.645 for the critical value for the 90% confidence interval. (If necessary, consult a list of formulas.)• 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 = 50.37.075% confidence interval|||||||37.051.5|||||||||||66.075% 75% 90% 90%lower upper lower upperlimit limit limit limit???S145.3?S2 48.2 44.2S3 52.4 48.4S4 47.7 43.7S5 52.3 48.3S6 43.3 39.3S7 43.4 39.452.2 42.5 53.956.4 46.7 58.151.7 42.0 53.456.3 46.6 58.047.3 37.6 49.047.4 37.7 49.1S8 56.5 52.5 60.5 50.862.2S9 47.2 43.251.2 41.552.951.753.442.053.2 43.5 54.947.5 37.8 49.2S10 47.7 43.7S11 49.2 45.2S12 43.5 39.5S13 45.2 41.2S14 51.3 47.3S15 48.4 44.449.2 39.5 50.955.3 45.6 57.052.4 42.7 54.1S16 51.7 47.7S17 51.6 47.655.7 46.0 57.455.6 45.9 57.358.7S18 54.7 50.749.0 60.4S19 48.8 44.852.8 43.1 54.5S20 47.2 43.2 51.2 41.5 52.937.066.037.0|++++++37.075% confidence intervals90% confidence interval(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n = 19 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.+|||||||||51.566.0 37.066.090% confidence intervals66.0||||||66,0 16(c) Notice that for20correct statement.= 80% of the samples, the 90% confidence interval contains the population mean. Choose theWhen constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% ofthe samples will contain the population mean.When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% ofthe samples must contain the population mean. There must have been an error with the way our samples werechosen.When constructing 90% confidence intervals for 20 samples of the same size from the population, the percentage ofthe samples that contain the population mean should be close to 90%, but it may not be exactly 90%.(d) Choose ALL that are true.The 75% confidence interval for Sample 15 indicates that 75% of the Sample 15 data values are between 44.4and 52.4.From the 90% confidence interval for Sample 15, we cannot say that there is a 90% probability that thepopulation mean is between 42.7 and 54.1.If there were a Sample 21 of size n=38 taken from the same population as Sample 15, then the 90% confidenceinterval for Sample 21 would be narrower than the 90% confidence interval for Sample 15.The 75% confidence interval for Sample 15 is narrower than the 90% confidence interval for Sample 15. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.None of the choices above are true.

Question

You have taken a random sample of size n = 19 from a normal population that has a population mean of μ = 50 and a population standard deviation of o=15.Your sample, which is Sample 1 in the table below, has a mean of x =45.3. (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 90% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidenceinterval, and use 1.645 for the critical value for the 90% confidence interval. (If necessary, consult a list of formulas.)• 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 = 50.37.075% confidence interval|||||||37.051.5|||||||||||66.075% 75% 90% 90%lower upper lower upperlimit limit limit limit???S145.3?S2 48.2 44.2S3 52.4 48.4S4 47.7 43.7S5 52.3 48.3S6 43.3 39.3S7 43.4 39.452.2 42.5 53.956.4 46.7 58.151.7 42.0 53.456.3 46.6 58.047.3 37.6 49.047.4 37.7 49.1S8 56.5 52.5 60.5 50.862.2S9 47.2 43.251.2 41.552.951.753.442.053.2 43.5 54.947.5 37.8 49.2S10 47.7 43.7S11 49.2 45.2S12 43.5 39.5S13 45.2 41.2S14 51.3 47.3S15 48.4 44.449.2 39.5 50.955.3 45.6 57.052.4 42.7 54.1S16 51.7 47.7S17 51.6 47.655.7 46.0 57.455.6 45.9 57.358.7S18 54.7 50.749.0 60.4S19 48.8 44.852.8 43.1 54.5S20 47.2 43.2 51.2 41.5 52.937.066.037.0|++++++37.075% confidence intervals90% confidence interval(b) Press the &#34;Generate Samples&#34; button below to simulate taking 19 more samples of size n = 19 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.+|||||||||51.566.0 37.066.090% confidence intervals66.0||||||66,0 16(c) Notice that for20correct statement.= 80% of the samples, the 90% confidence interval contains the population mean. Choose theWhen constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% ofthe samples will contain the population mean.When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% ofthe samples must contain the population mean. There must have been an error with the way our samples werechosen.When constructing 90% confidence intervals for 20 samples of the same size from the population, the percentage ofthe samples that contain the population mean should be close to 90%, but it may not be exactly 90%.(d) Choose ALL that are true.The 75% confidence interval for Sample 15 indicates that 75% of the Sample 15 data values are between 44.4and 52.4.From the 90% confidence interval for Sample 15, we cannot say that there is a 90% probability that thepopulation mean is between 42.7 and 54.1.If there were a Sample 21 of size n=38 taken from the same population as Sample 15, then the 90% confidenceinterval for Sample 21 would be narrower than the 90% confidence interval for Sample 15.The 75% confidence interval for Sample 15 is narrower than the 90% confidence interval for Sample 15. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.None of the choices above are true.

Accepted Answer

Here we have give that,sample size = n = 19Population Mean = µ = 50Population Standard Deviation = σ…