Suppos ✓ are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of G=5. We have taken a random sample of size = 10 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 I=99.3. 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 = 100, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size = 10 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. 75% 90% 90% 75% I lower upper lower upper limit limit limit limit 97.5 101.1 96.7 101.9 51 99.3 52 99.5 97.7 53 98.9 97.1 100.7 96.3 101.3 96.9 102.1 101.5 54 99.1 97.3 100.9 96.5 101.7 55 97.0 95.2 98.8 94.4 99.6 56 98.9 97.1 100.7 96.3 101.5 57 99.3 97.5 101.1 96.7 101.9 58 101.1 99.3 102.9 98.5 103.7 59 97.8 96.0 99.6 95.2 100.4 $10 101.1 99.3 102.9 98.5 103.7 sai 1011 593 |1029| 935 | 102.7 S12 97.8 96.0 99.6 95.2 100.4 S13 98.9 97.1 100.7 96.3 101.5 S14 100.6 98.8 1024 98.0 103.2 $15 100.8 99.0 102.6 98.2 103.4 S16 101.2 99.4 103.0 98.6 103.8 S17 102.2 100.4 104.0 99.6 104.8 S18 101.1 99.3 102.9 98.5 103.7 $19 99.9 98.1 101.7 97.3 102.5 s20 100.3 98.5 102.1 97.7 102.9 94.0 75% confidence intervals 106.0 94.0 90% confidence intervals 106.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 100? (b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, μ = 100? x

A notable indicator of a baby's health is the weight gained in the first year of the baby's life. Assume that the population of all such weight gains for baby boys is approximately normally distributed. A study claimed that the mean of this population is 4.93 kg. As a practicing pediatrician, you want to test this claim. So, you select a random sample of 16 baby boys, and you record the weight each gained in their first year. Follow the steps below to construct a 99% confidence interval for the population mean of all the weight gains for baby boys in their first year. Then state whether the confidence interval you construct contradicts the study's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. Sample standard Number of baby boys Sample mean deviation Take Sample 16 5.496 1.873 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for…

Jeremiah earned a score of 530 on Exam A that had a mean of 450 and a standard deviation of 40. He is about to take Exam B that has a mean of 63 and a standard deviation of 20. How well must Jeremiah score on Exam B in order to do equivalently well as he did on Exam A? Assume that scores on each exam are normally distributed.

A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100. A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15. Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance?   Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and why