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Hypothesis Testing Review - 2 Questions

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An investment services company claims that the average annual return on stocks within a certain industry is 11.5%. An investor wants to test whether this claim is true and collects a random sample of 50 stocks in the industry of interest. He finds that the sample average annual return is 10.8% and that the sample standard deviation is 3.4%. Does the investor have enough evidence to reject the investment company's claim? (Use a 5% significance level.)

The average weekly earnings for all full-time-equivalent employees are reported to be $344. Suppose you want to check this claim since you believe it is too low. You want to provide evidence that the average weekly earnings of all employees are higher than the amount claimed. You collect a random sample of 1,200 employees in all areas and find that the sample mean is $361 and the sample standard deviation is $110. Can you reject the claim?

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Solution Summary

Review of hypothesis testing using examples of investor claims and average weekly earnings attached as a Word document.

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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