Suppose that a random sample of 20 adults has a mean score of 80 on a standardized personality test, with a standard deviation of 5. (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 95% confidence interval for the mean score of all takers of this test. Give the lower limit and upper limit of the 95% confidence interval.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit: Upper limit:

The standard deviation of test scores on a certain achievement test is 11.3. A random sample of 50 scores on this test had a mean of 75.9. Based on this sample, find a 95% confidence interval for the true mean of all scores. Then give its lower limit and upper limit.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit: Upper limit:

A psychologist is interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of 16. The psychologist randomly selects 80 children from this group and finds that their mean IQ score is 110. Based on this sample, find a 90% confidence interval for the true mean IQ score for all children of this group. Then give its lower limit and upper limit.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit: Upper limit:

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.

Scores on a recent Statistics test are normally distributed with a standard deviation of 6.5 points. If the professor wants to estimate the population mean test score within 1 point with 90% confidence, what sample size is needed

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.