You have taken a random sample of size =n22 from a normal population that has a population mean of =μ95 and a population standard deviation of =σ8. Your sample, which is Sample 1 in the table below, has a mean of =x93.9. (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% confidence interval, 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, =μ95.75% confidence interval87.0102.0 90% confidence interval87.0102.0(b)Press the "Generate Samples" button below to simulate taking 19 more samples of size =n22 from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.x 75%lowerlimit 75%upperlimit 90%lowerlimit 90%upperlimitS1 93.9 ? ? ? ?S2 94.8 92.8 96.8 92.0 97.6S3 94.5 92.5 96.5 91.7 97.3S4 98.7 96.7 100.7 95.9 101.5S5 94.3 92.3 96.3 91.5 97.1S6 94.6 92.6 96.6 91.8 97.4S7 94.6 92.6 96.6 91.8 97.4S8 95.8 93.8 97.8 93.0 98.6S9 97.4 95.4 99.4 94.6 100.2S10 96.1 94.1 98.1 93.3 98.9S11 92.6 90.6 94.6 89.8 95.4S12 96.0 94.0 98.0 93.2 98.8S13 94.5 92.5 96.5 91.7 97.3S14 91.1 89.1 93.1 88.3 93.9S15 96.2 94.2 98.2 93.4 99.0S16 91.4 89.4 93.4 88.6 94.2S17 96.0 94.0 98.0 93.2 98.8S18 94.1 92.1 96.1 91.3 96.9S19 94.2 92.2 96.2 91.4 97.0S20 94.1 92.1 96.1 91.3 96.975% confidence intervals87.0102.090% confidence intervals87.0102.0(c)Notice that for =172085% of the samples, the 90% confidence interval contains the population mean. Choose the correct statement. When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% of the samples will contain the population mean. When constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% of the samples will contain the population mean. When constructing 90% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 90% of the samples will contain the population mean.(d)Choose ALL that are true. The 90% confidence interval for Sample 8 does not indicate that 90% of the Sample 8 data values are between 93.0 and 98.6. The 75% confidence interval for Sample 8 is narrower than the 90% confidence interval for Sample 8. This must be the case, because when a confidence interval is constructed for a sample, the greater the level of confidence, the wider the confidence interval. From the 75% confidence interval for Sample 8, we know that there is a 75% probability that the population mean is between 93.8 and 97.8. If there were a Sample 21 of size =n44 taken from the same population as Sample 8, then the 90% confidence interval for Sample 21 would be narrower than the 90% confidence interval for Sample 8. None of the choices above are true.

A sample of size =n90 is drawn from a normal population whose standard deviation is =σ9.7. The sample mean is =x38.78.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct an 80% confidence interval for μ. Round the answer to at least two decimal places.An 80% confidence interval for the mean is <<μ.

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.

A random sample of size n1 = 25, taken from a normal population with a standard deviation σ1 = 5, has a mean ¯x1 = 80. A second random sample of size n2 = 36, taken from a different normal population with a standard deviation σ2 = 3, has a mean ¯x2 = 75. Find a 94% confidence interval for μ1 − μ2.

You want to compute a 90% confidence interval for the mean of a population with unknown standard deviation. The sample size is 30. The correct distribution value for calculating the required confidence interval is:-Group of answer choices1.961.64491.6991.6971.311

a. Find a 98% confidence interval for the mean μ of a normal population withvariance 9 from the sample 32,42,41,35,48,55.b. Find a 98% confidence interval for the mean μ of a normal population from thesample 32,42,41,35,48,55.c. Using a sample size n = 15 and a sample variance s2 = 13 from a normalpopulation , test the hypothesis σ2 = σ02 = 10 against three kinds of alternatives,namely, a σ2 < σ02b σ2 > σ02c σ2 ≠ σ02by choosing a significance level 1%.