You have taken a random sample of size =n80 from a normal population that has a population mean of =μ60 and a population standard deviation of =σ16. Your sample, which is Sample 1 in the table below, has a mean of =x62.7. (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% confidence interval, and use 1.960 for the critical value for the 95% 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, =μ60.75% confidence interval51.068.0 95% confidence interval51.068.0(b)Press the "Generate Samples" button below to simulate taking 19 more samples of size =n80 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 95%lowerlimit 95%upperlimitS1 62.7 ? ? ? ?S2 58.9 56.8 61.0 55.4 62.4S3 61.1 59.0 63.2 57.6 64.6S4 58.9 56.8 61.0 55.4 62.4S5 61.3 59.2 63.4 57.8 64.8S6 64.1 62.0 66.2 60.6 67.6S7 57.1 55.0 59.2 53.6 60.6S8 57.2 55.1 59.3 53.7 60.7S9 59.9 57.8 62.0 56.4 63.4S10 60.3 58.2 62.4 56.8 63.8S11 64.2 62.1 66.3 60.7 67.7S12 61.1 59.0 63.2 57.6 64.6S13 59.3 57.2 61.4 55.8 62.8S14 61.2 59.1 63.3 57.7 64.7S15 58.5 56.4 60.6 55.0 62.0S16 60.5 58.4 62.6 57.0 64.0S17 62.8 60.7 64.9 59.3 66.3S18 57.1 55.0 59.2 53.6 60.6S19 59.8 57.7 61.9 56.3 63.3S20 60.7 58.6 62.8 57.2 64.275% confidence intervals51.068.095% confidence intervals51.068.0(c)Notice that for =182090% of the samples, the 95% confidence interval contains the population mean. Choose the correct statement. When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples must contain the population mean. There must have been an error with the way our samples were chosen. When constructing 95% confidence intervals for 20 samples of the same size from the population, the percentage of the samples that contain the population mean should be close to 95%, but it may not be exactly 95%. When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean.(d)Choose ALL that are true. The 75% confidence interval for Sample 5 indicates that 75% of the Sample 5 data values are between 59.2 and 63.4. From the 95% confidence interval for Sample 5, we cannot say that there is a 95% probability that the population mean is between 57.8 and 64.8. The 75% confidence interval for Sample 5 is narrower than the 95% confidence interval for Sample 5. 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. If there were a Sample 21 of size =n160 taken from the same population as Sample 5, then the 95% confidence interval for Sample 21 would be wider than the 95% confidence interval for Sample 5. None of the choices above are true.CheckSave For LaterSubmit Assignment

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 sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use  t Distribution Table & z Distribution Table.)Required:a. Determine the standard error of the mean. (Round your answer to 3 decimal places.)c. Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)