Appendix B Data Sets
In Exercises 29–32, use the data fr...

Question

Appendix B Data Sets

In Exercises 29–32, use the data from Appendix B to construct a scatterplot, find the value of the linear correlation coefficient r, and find either the P-value or the critical values of r from Table A-6 using a significance level of α = 0.05. Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

Taxis Repeat Exercise 15 using all of the time/tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. Compare the results to those found in Exercise 15.

Accepted Answer

Hello everyone. Let's take a look at this question together. An economist examines the relationship between the number of years of work experience X and annual salary Y for 30 employees in a company. The calculated linear correlation coefficient is R equals 0.58. At a significance level of alpha equals 0.05, is there enough evidence to claim a linear correlation between years of experience and annual salary? So in order to determine whether there is enough evidence to claim a linear correlation between years of experience X and annual. we can perform a hypothesis test for the population correlation coefficient row, which the first step in solving this problem is to state the hypotheses where the null hypothesis is row equals 0 and the alternative hypothesis is row does not equal 0. Then we calculate the test statistic. By using a T distribution to test the significance of the correlation coefficient. So the test statistic T is equal to R multiplied by the square root of N minus 2, divided by the square root of 1 minus R squad. Which for this formula, R is equal to 0.58 as it is our sample correlation, and N is equal to 30 as it is our sample size. And plugging in our values into the formula for the test statistic, our T value is approximately 3.77. Then we calculate our degrees of freedom and the critical value, starting with our degrees of freedom, which is equal to N minus 2, so it is 28. And we know that our significance level is alpha equals 005, so this is a two-tailed test, as this is a two-tailed test, and so using a T distribution table, the critical value for a degree of freedom equal to 28 and an alpha equal to 0.05 is approximately positive or negative. 2.048. So now we can make our decision, which is that if the absolute value of T is greater than our T critical value, we reject the null hypothesis. And since the absolute value of T, which is equal to 3.77, is greater than 2.048, we reject the null hypothesis. So in conclusion, at the 0.05 significance level, there is sufficient evidence to conclude that a linear correlation exists between years of work experience, and annual salary. Therefore, answer choice C is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Scatterplot

Linear Correlation Coefficient (r)

P-value and Significance Level

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