Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 36 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that μ is greater than 36 minutes. The consultant plans to do a statistical test and collects a random sample of 50 shopping times at the supermarkets.Suppose that the population of shopping times at the supermarkets has a standard deviation of 16 minutes and that the consultant performs her hypothesis test using the 0.05 level of significance. н. :р isWhat are the null and alternative hypotheses that theconsultant should use for the test?H, :H isWhat is the probability that the consultant commits aType I error? Round your response to at least twodecimal places.Assuming that the actual value of u is 41 minutes, whatis the power of the test? Round your response to at least||two decimal places.The probability of committing a Type II error in the secondtest is greaterSuppose that the consultant decides to perform anotherstatistical test using the same population, the same nulland alternative hypotheses, and the same level ofsignificance, but for this second test the consultantchooses a random sample of size 150 instead of arandom sample of size 50. Assuming that the actualvalue of u is 41 minutes, how does the probability thatthe consultant commits a Type II error in this secondtest compare to the probability that the consultantcommits a Type II error in the original test?The probability of committing a Type II error in the secondtest is lessThe probabilities of committing a Type II error are equal

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Description: Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 36 minutes, but executives hire

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time,

, spent by customers at the supermarkets has been reported to be

minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that

is greater than

minutes. The consultant plans to do a statistical test and collects a random sample of

shopping times at the supermarkets.

Suppose that the population of shopping times at the supermarkets has a standard deviation of

minutes and that the consultant performs her hypothesis test using the

0.05

level of significance.

н. :р is
What are the null and alternative hypotheses that the
consultant should use for the test?
H, :H is
What is the probability that the consultant commits a
Type I error? Round your response to at least two
decimal places.
Assuming that the actual value of u is 41 minutes, what
is the power of the test? Round your response to at least||
two decimal places.
The probability of committing a Type II error in the second
test is greater
Suppose that the consultant decides to perform another
statistical test using the same population, the same null
and alternative hypotheses, and the same level of
significance, but for this second test the consultant
chooses a random sample of size 150 instead of a
random sample of size 50. Assuming that the actual
value of u is 41 minutes, how does the probability that
the consultant commits a Type II error in this second
test compare to the probability that the consultant
commits a Type II error in the original test?
The probability of committing a Type II error in the second
test is less
The probabilities of committing a Type II error are equal

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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