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Null Hypotheses

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Problem (Null Hypothesis)

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was $8.16, and there is reason to believe that this year's value is different from last year's.
The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be $7.79, and computes the standard deviation of the sample to be $1.20.

Question

What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?
-H0: mu = (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16)
-H1: mu= (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16)
In the context of this test, what Type I error?
-A Type I error is (rejecting, failing to reject) the hypothesis that mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16) when, in fact, mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16).
-Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making? (Type I, Type II)

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Solution Summary

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was $8.16, and there is reason to believe that this year's value is different from last year's.

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Problem (Null Hypothesis)

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was $8.16, and there is reason to believe that this year's value is different from last year's.
The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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