2. An investment consultation firm claims that it will increase the returns on its clients' investments to a.average of 20% of the original investments, with minimal risk involved. In a random sample of 50clients of the firm, the average return on investments with minimal risk was 18.5% of the originalinvestment, with a standard deviation of 0.5%.a. Find the z-value, rounded to the nearest hundredth.b. Is there enough evidence to reject the firm's claim?

Given that Sample size n =50 Sample mean =18.5 Standard deviation =0.5

Answered: 2. An investment consultation firm…

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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After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college students is taken and the sample mean and sample standard deviation are found to be 21.5 years and 2.3 years, respectively. a.Is the sample average of 21.5 considered an outlier (in other words, what is the chance of getting a sample mean at least as large as 21.5 assuming μ and σ are correct)? b. The calculated value of the sample standard deviation is larger than σ, is 2.3 years enough larger than 1.8 that the estimate of σ does not seem reasonable? Use probability to support your conclusion c.No matter what you got for an answer in part b, assume we no longer trust σ = 1.8 to be valid. Calculate the same probability as you did in part a, but this time, assume that σ is unknown.
3. A medical statistician wants to estimate average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses σ is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds with 95% confidence?
An insurance company wants to make sure that its best customers (those with lowest value of insurance claims) stay with the company. To achieve this goal, the company plans to offer a 10% discount on the annual health insurance premium for customers with the lowest 20% of annual health care expenses. If the average annual health care expenses for a family of four is $3,650 with a standard deviation of $975, what is the amount of the maximum annual health care expense that will qualify for the proposed discount?
1.In a certain wildlife reserve the life span of monkey are normally distributed. The average monkey lives 20.8 years and The standard deviation is 3.1 years. Use the empirical rule to estimate the probability or percentage of a monkey living less than 23.9 years. 2. If the population of the monkey are 568, how many of them will live for less than 23.9 years. 3. IQ scores which are normallu distributed have a mean of 100 and a standard deviation of 16. The z score that corresponds to Albert IQ Is 3.75. What is his IQ?
E
4. Find the 90% confidence interval for the variance and standard deviation for the time it takes a telephone company to transfer a call to the correct office. A sample of 15 calls has a standard deviation of 1.6 minutes. Assume the variable is normally distributed. 5.00
From a sample with n = 12, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 0 and 4 televisions. At least of the households have between 0 and 4 televisions. (Simplify your answer.)
12. Callahan (2009) demonstrated that tai chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctordiagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an eight-week tai chi course and again at the end. Suppose that the data produced an average decrease in pain and stiffness of MD= 8.5 points with a standard deviation of 21.5 for a sample of n= 40 participants. a. Use a two-tailed test with alpha= .05 to determine whether the tai chi had a significant effect on pain and stiffness. b. Compute Cohen’s d to measure the size of the treatment effect.
Suppose that the amount of protein in certain type of energy bar is Normally Distributed with a mean of 8.1 grams with a standard deviation of 0.64 grams. Suppose that a random bar of this type is selected. c. Find the probability that a bar has less than 8.9 grams of protein. d. Find the 90th percentile of the grams of protein in these bars. e. Find the values v and w such that the middle 90% of protein amounts fall between v and w
a. State the null and alternative hypothesis.
3. A local hospital doctor's team reports that the average cost of treatment of heart disease is 800 RO. To see if the average cost of treatment is different at a particular hospital, a researcher selected a random sample of 40 patients and found that the average cost of treatment is 400 RO. The standard deviation of the population is 350 RO. At test the claim of the hospital doctors.

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