Answered: A union of restaurant and foodservice…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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A union of restaurant and foodservice workers would like to estimate the mean hourly wage, μ, of foodservice workers in the U.S. this year The mean hourly wage last year was $8.14, and there is good reason to believe that this year's value is greater than last year's.The union decides to do a statistical test to see if the value has indeed increased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $8.44, and computes the standard deviation of the sample to be$1.10.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making?
	▼(Choose one)
(c)	Suppose the true mean hourly wage for foodservice workers in the U.S. this year is $8.14. Fill in the blanks to describe a Type I error.
A Type I error would be ▼(Choose one) the hypothesis that μ is ▼(Choose one) ▼(Choose one)when, in fact, μ is ▼(Choose one) .

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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