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# Correlation and Hypothesis Testing

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1. Using data consisting of diamond price and carat (weight) for thirty randomly selected diamonds, a correlation between price and weight was found to be 0.767. At the 0.01 level of significance, is there a positive association between the two variables? Show all 5 steps in the hypothesis testing process.

2. Kendra Korbin, owner and operator of Cyber Video Game Store, records her business costs and revenue for different years, with the results listed below.

Amount invested
(thousands of dollars) 1 2 5 11 20 31 41 46 48
Revenue (dollars) 2001 2639 3807 5219 6629 7899 8834 9250 9409

a. Construct a scatter plot of the data.
b. Based on the plot from part a, does linear regression appear to be an appropriate technique? Why or why not?

##### Solution Summary

The correlation and hypothesis testing are examined.

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###### 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!"

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.