(a) How many of the 80% confidence intervals constructed from the 20 samples contain the population mean, μ = 105?(b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 105?(c) Choose ALL that are true.The center of the 80% confidence interval for Sample 1 is 106.4, because the center of a confidence interval for thepopulation mean must be the sample mean.□ All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there musthave been errors due to rounding.Since Sample 19 and Sample 20 are drawn from the same population, the center of the 95% confidence interval forSample 19 must be the same as the center of the 95% confidence interval for Sample 20.For each sample, the 80% confidence interval for the sample is included in the 95% confidence interval for thesample.None of the choices above are true. Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of = 19. We have taken arandom sample of size n = 87 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 x = 106.4. Also shown are the lower and upper limits of the 80% confidence interval for the populationmean 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 u = 105, which isshown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 87 from this same population. (The 80% and 95% confidenceintervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.80% 80% 95% 95%lower upper lower upperlimit limit limit limit110.4S1 106.4 103.8 109.0 102.4S2 104.5 101.9 107.1 100.5 108.5S3 106.1 103.5 108.7 102.1 110.154 108.3 105.7 110.9 104.3 112.3S5 103.6 101.0 106.2 99.6 107.6S6 104.5 101.9 107.1 100.5 108.5S7 106.4 103.8 109.0 102.4 110.4S8 103.7 101.1 106.3 99.7 107.759 108.5 105.9 111.1 104.5 112.5$10 109.8 107.2 112.4 105.8 113.8|511 104.6|102.0 | 107.2 | 100.6 | 108.6S12 104.1 101.5106.7 100.1 108.1S13 101.5 98.9 104.1 97.5 105.5S14 103.4 100.8 106.0 99.4 107.4$15 105.5 102.9 108.1 101.5 109.5S16 101.7 99.1 104.3 97.7 105.7S17 107.3 104.7 109.9 103.3 111.3S18 100.4 97.8 103.0 96.4 104.4$19 105.6 103.0 108.2 101.6 109.6S20 106.5 103.9 109.1 102.5 110.5xH96.080% confidence intervals++H114.0 96.095% confidence intervalsWAN++114.0

It is given that Sample size n = 87 Population SD = 19 Confidence level = 80%, 95%. True population…

Answered: (a) How many of the 80% confidence…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Construct a 95% and 99% confidence interval of the age of adults with at most 3 vaccine shots. Compare the marginsof error for intervals. Base from your answers, make an inference in one or two sentences only.
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Part a) Find the 68% confidence interval for the percentage of leaky diapers in Example 4.4.4. Note that it is 8 percentage points long. Part b) Find the 95% confidence interval for the percentage of leaky diapers in Example 4.4.4 assuming 200 diapers were tested and 20% were leaky. Note that it is not 8 percentage points long. Part c) Find the 95% confidence interval for the percentage of leaky diapers in Example 4.4.4 assuming 400 diapers were tested and 20% were leaky. Note that it is 8 percentage points long.Also, for exercise 40, fair means that heads happens with probability 0.5. Asking if a coin is fair is asking whether 0.5 is inside the confidence interval. The diaper manufacturer of Example 4.4.4, page 149, decides that theconfidence interval obtained is too wide, at 16 percentage points. Hewould like to narrow it to half the width, i.e. 8 percentages points.(Hint: you may want to use the results of Exercise 38.) a) Show that reducing the confidence level to 68%, he can get…
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Echinacea is widely used as an herbal remedy for the common cold, but does it work? In a double-blind experiment, healthy volunteers agreed to be exposed to common-cold-causing rhinovirus type 39 and have their symptoms monitored. The volunteers were randomly assigned to take either a placebo or an echinacea supplement daily for 5 days following viral exposure. Among the 103 subjects taking a placebo, 88 developed a cold, whereas 44 of the 48 subjects taking echinacea 1 developed a cold.
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