Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of =σ5. We have taken a random sample of size =n10 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 =x101.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean 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 =μ100, which is shown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size =n10 from this same population. (The 75% and 90% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.x 75%lowerlimit 75%upperlimit 90%lowerlimit 90%upperlimitS1 101.1 99.3 102.9 98.5 103.7S2 Generate SamplesS3S4S5S6S7S8S9S10S11S12S13S14S15S16S17S18S19S2075% confidence intervals94.0106.090% confidence intervals94.0106.0(a)How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, =μ100? (b)How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, =μ100? (c)Choose ALL that are true. For each sample, the 75% confidence interval for the sample is included in the 90% confidence interval for the sample. It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval for Sample 19 is different from the center of the 90% confidence interval for Sample 20. We would expect to find more 75% confidence intervals that contain the population mean than 90% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval. None of the choices above are true.

A population is known to have a population standard deviation o=4.A sample of size n=64 is drawn.The sample mean is 21.4 and sample standard deviation is 4.1. The lower limit of the 95%confidence interval is

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.

Which confidence level would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population?A.26%B.54%C.11%D.38%

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 population's standard deviation is 12. We want to estimate the population mean with a margin of error of 2, with a 95% level of confidence. (Use t Distribution Table & z Distribution Table.)How large a sample is required? (Round your intermediate calculations to 2 decimal places and round up your answer to the next whole number.)