Homework Help is Here – Start Your Trial Now!
Math
Statistics
A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.25, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has decreased. The union chooses random sample of 50 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.18 and that the union performs its hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the union should use for the test? Ho: µ = 8.25 H: µ < 8.25 (b) Assuming that the actual value of u is $7.80, what is the probability that the union commits a Type Il error? Round your response to two or more decimal places. O=0 OSO O

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.25, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has decreased. The union chooses random sample of 50 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.18 and that the union performs its hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the union should use for the test? Ho: µ = 8.25 H: µ < 8.25 (b) Assuming that the actual value of u is $7.80, what is the probability that the union commits a Type Il error? Round your response to two or more decimal places. O=0 OSO O

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
See similar textbooks
icon
Related questions
Question

I'm not sure how to figure out this problem. I have attached pictures below.

(d) Suppose that the union 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 union chooses a random sample of size 100 instead of a random sample of size 50. Assuming that the actual value of u is $7.80, how does the power of this second test compare to the power of the original test? OThe power of the second test is greater than the power of the original test OThe power of the second test is less than the power of the original test OThe powers of the two tests are equal
Transcribed Image Text:(d) Suppose that the union 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 union chooses a random sample of size 100 instead of a random sample of size 50. Assuming that the actual value of u is $7.80, how does the power of this second test compare to the power of the original test? OThe power of the second test is greater than the power of the original test OThe power of the second test is less than the power of the original test OThe powers of the two tests are equal
A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.25, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has decreased. The union chooses a random sample of 50 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.18 and that the union performs its hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the union p should use for the test? Ho: µ = 8.25 H: µ < 8.25 (b) Assuming that the actual value of u is $7.80, what is the probability that the union O=0 OSO commits a Type Il error? Round your response to two or more decimal places. O<O (c) What is the probability that the union rejects the null hypothesis when, in fact, it is true? Round your response to two or more decimal places.
Transcribed Image Text:A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.25, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has decreased. The union chooses a random sample of 50 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.18 and that the union performs its hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the union p should use for the test? Ho: µ = 8.25 H: µ < 8.25 (b) Assuming that the actual value of u is $7.80, what is the probability that the union O=0 OSO commits a Type Il error? Round your response to two or more decimal places. O<O (c) What is the probability that the union rejects the null hypothesis when, in fact, it is true? Round your response to two or more decimal places.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS