# Testing hypotheses based on a given data set

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Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective homebuyers in the Middletown and Brockton areas of the city. One item of interest is the number of years that children remain in the same district for schooling. A sample of 40 households with school-aged children in Middletown was randomly selected. The mean length of time was 7.6 years, with a standard deviation of 2.3 years. A sample of 55 households in Brockton revealed the mean length of time was 8.1 years, with a standard deviation of 2.9 years. At the .05 level of significance, can we conclude the Middletown students stayed in their districts less time than the Brockton students? Use the 5-step hypothesis testing procedure

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##### Solution Summary

The solution contains detailed explanation of testing hypotheses using the five-step procedure.

###### 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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