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Comparing Mean Annual Incomes of Teachers

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Past records suggest that the mean annual income, mu1, of teachers in state of Arizona is greater than or equal to the mean annual income, mu2, of teachers in Nevada. In a current study, a random sample of 20 teachers from Arizona and an independent random sample of 20 teachers from Nevada have been asked to report their mean annual income.The data obtained are as follows.

Annual income in dollars
Arizona
48303,33944,40726,33817,28847,45779,38982,36947,34453,39765,42384,
43941,29673,33219,41164,37954,36804,39312,44525,33572

Nevada
44780,40971,36770,39739,37583,41542,48342,46483,51735,38833,48769,
49958,41041,34853,36057,54812,39022,47245,44511,47733

The population standard deviation for mean annual income of teachers in Arizona and in Nevada are estimated as 6300 and 6500, respectively. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Arizona is greater than or equal to the mean annual income of teachers in Nevada? Perform a one-tailed test. Please provide answers as requested below.

Carry your intermediate computations to at least three decimal places and round your answers as specified.

1. The null hypothesis value Ho=

2. The alternative hypothesis value H1=

3. The type of test statistic used(choose one) Z, t and degrees of freedom, chi square and degrees of freedom, F and the dfn and dfd.

4. The value of the test statistic (Round to at least 3 decimal places)

5. The critical value at the 0.05 level of significance(Round to at least 3 decimal places)

6. Can we reject the claim that the mean annual income of teachers from Arizona is greater than or equal to the mean annual income of teachers from Nevada? Yes or No

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Solution Summary

Word document and Excel files show how to accurately compare teacher incomes across states.

Solution provided by:
Changping Wang, MA
Education
  • 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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