(a) Suppose a random sample of size n =has sample mean x 50 and sample variance s225 from a normal population with unknown variance= 64.%3DConstruct a 100(1-a)% Confidence Interval (C.I.) for the population meana = 0.10, a = 0.05 and a = 0.01.withi)%3DFind the lengths of the intervals constructed above. What is the relationship between theconfidence level (1- a) and the length of C.L.?

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Answered: (a) Suppose a random sample of size n=…

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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#21)
Data indicates that adolescent girls tend to experience a drop in self-esteem. To evaluate this result, a researcher obtains a sample of N = 36 adolescent girls, all 13 years old. A self-esteem measure is administered to each participant and the average score for the sample is X =68. It is known that the distribution of self-esteem scores for the population of pre-teen girls is normal with mean 80 and standard deviation 10. (a) Compute a 95% confidence interval for µ, the population mean self-esteem score for adolescent girls. (b) Compute Cohen’s d to estimate the size of the described effect. (c) Perform a hypothesis test to decide whether the mean self-esteem score for adolescent girls is significantly different from the mean self-esteem score for pre-teen girls. (d) Compute and interpret a Bayes factor for the model (either H0 or H1) with the best predictive adequacy. (e) Compute and interpret the posterior model probability for the winning model chosen in part (d).
Suppose the retirement age in the U.S. is normally distributed with an unknown population mean and standard deviation. A random sample of 22 retirees is taken and results in a sample mean of 59 years old and sample standard deviation of 5 years.The margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution is 2.22. Find a 95% confidence interval estimate for the population mean using the Student's t-distribution. Round the final answers to two decimal places
A researcher is interested in studying the use of hypnosis to relieve pain. She took a random sample of 16 subjects and measured their sensory ratings. The mean of the sensory ratings was found to be 7.5 and standard deviation to be 2.3. It is known that the sensory ratings are normally distributed. Construct a 99% confidence interval for the mean sensory ratings of the population. a) (5.81, 9.19) b) (6.27, 8.73) c) (6.36, 8.64) d) (6.02, 8.98)
#4data: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Use the sample data from #4 to construct a 98% confidence interval estimate for the standard deviation of the amount nitrogen-oxide emission for all cars.
A sample of n=41n=41 data values randomly selected from a normally distributed population has variance s2=30s2=30. Construct a 95% confidence interval for the population variance. Round your endpoints to one decimal place.
The mean test score for a simple random sample of n=100 students was =80. The population standard deviation of test scores is σ=15. Construct a 95% confidence interval for the population mean test score μ.
A sample of 14 male college students consumes an average of 14.3 gallons of beer per month, with a sample standard deviation of 5.2 gallons. You can safely assume that the population of monthly beer consumption is Normally distributed. What is the margin of error for a 90% Confidence Interval for the mean? (Leave your answer to two decimal places, ex: 18.12)
The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of 22 car batteries. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values…
You are going to create a 99% confidence interval for the mean amount ofsugar in coffee shop specialty drinks. You know the population standarddeviation is σ = 5.9 grams. You want your confidence interval to have amargin of error of 0.25 grams. How big should your sample size be to obtainthis margin of error?

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