Answered: #9. Executives of a supermarket chain… | bartleby

MATLAB: An Introduction with Applications

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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#9. Executives of a supermarket chain are interested in the amount of time customers been in the stores during shopping trips the executives hire a statistical consultant and ask her to determine the mean shopping time, U (population mean), of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarket and use the mean of the shopping times to estimate U (population mean) . Assuming that the state of deviation of the population of shopping times at the supermarket is 27 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 4 minutes of U. Carrier, intermediate, computations to at least three decimal places write your answer as a whole number, and make sure that it is the minimum whole number that satisfies the requirement .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 3% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.Round your answer to the nearest minute.
Manatees are one creature found in coastal waterways. 10 years ago, researchers concluded that the true mean weight of manatees was approximately 1050 lbs. This year, a random sample of 12 manatees were selected, the sample weights are: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assume the underlying distribution of manatee weights is normal, and population standard deviation o is unknown. Implement a hypothesis test to verify if there is any evidence to suggest the true mean weight decreases now. Solve the hypothesis using P-value method. Let a = 0.05. . Use the given sample data to calculate 90% confidence interval for true mean weight of manatees.

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