The number of miles ridden until a rental bicycle gets a flat tire is modelled as an Exponential(2) random variable. A Gamma(α=4.0, ß= 120.0) prior for was selected. A random sample of n = 5 flats had the following distances travelled between the occurrences of flats: 8.0, 42.2, 16.8, 44.8, 10 Find a Normal Approximation, Normal(µ, o²), (expectation µ and standard deviation ♂) to the posterior distribution for where μ = and o =
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- Let m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.Find the corresponding z-score for a sample of n = 16 and M = 38 taken from a population with a mean of μ= 40 and σ = 8.
- You obtain a t comp of .975 in a two sample independent t test with alpha at .05. Is it significant?8.4.1B. In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 51 subjects wore magnetic insoles and 43 subjects wore nonmagnetic insoles. The results are shown at the right. At α=0.06, can you support the claim that there is a difference in the proportion of subjects who feel better between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Do you Feel Better? A circle graph titled Magnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows: Yes, 15, 29.41 percent; No, 36, 70.59 percent. Magnetic Insoles Yes 15No 36 A circle graph titled Nonmagnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows: Yes, 21, 48.84 percent; No, 22, 51.16 percent. Nonmagnetic Insoles Yes 21No 22 (b) Find the critical value(s) and identify the rejection region(s). The…A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 215 225 235 240 255 260 225 Total Blood Cholesterol (After) 214 222 240 237 254 257 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μd=μ1−μ2. Choose the correct…
- Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A random sample of size 36 from a population with known variance, o = 9, yields a sample mean of x = 17. Find ß, for testing the hypothesis H,: u = 15 versus H1 : =16. Assume a 0.05. %3D %3DA sample of n=25 scores has a mean of M=68. Find the z-score for this sample: If it was obtained from a population with m=60 and s=10. If it was obtained from a population with m=60 and s=20. If it was obtained from a population with m=60 and s=40. A normal distribution has a mean of μ = 54 and a standard deviation of σ = 6. What is the probability of randomly selecting a score less than X = 51? What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51? What is the probability of selecting a sample of n = 36 scores with a mean less than M = 51? A sample is selected from a population with a mean of and a standard deviation of . If the sample has scores, what is the expected value of and the standard error of If the sample has scores, what is the expected value of and the standard error of ? A random sample is obtained from a normal population with a mean of and a standard deviation of . The sample mean is Is this a…6.2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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