A random sample of 10 professional athletes produced the following data where X is the number of endorsements the player has and Y is the amount of money made (in millions of dollars).Use the 4 steps of hypothesis testing to see if the prediction is significant with a criteria of alpha=.05 on the following data.xy02382713513512493903410

Solution: The data on X: the number of endorsements the player has and Y: the amount of money made (in millions of dollars) is given. It is asked to test if the prediction is significant with a criteria of alpha=.05 Level of significance: α = 0.05 For that, we will do a slope test. The null and alternative hypotheses for this test are: Before finding the test statistic, we will find the coefficients of the least squares regression line using MS-Excel. Enter the given data in excel such that x values are entered from A2 to A11 and y values are entered from B2 to B11. For Intercept: Type =INTERCEPT(B2:B11, A2:A11) and hit enter. It gives 2.233645. Thus, intercept: b0 = 2.233645 For slope: Type =SLOPE(B1:B11, A2:A11) and hit enter. It gives 1.987539 Thus, slope: b1 = 1.987539 Thus, the least squares regression equation becomes Test statistic: We will make the following table to find the squares of residuals. x y yhat y-yhat (y-yhat)2 0 2 2.233645 -0.23364 0.05459 3 8 8.196262 -0.19626 0.038519 2 7 6.208723 0.791277 0.62612 1 3 4.221184 -1.22118 1.49129 5 13 12.17134 0.82866 0.686678 5 12 12.17134 -0.17134 0.029357 4 9 10.1838 -1.1838 1.401384 3 9 8.196262 0.803738 0.645995 0 3 2.233645 0.766355 0.5873 4 10 10.1838 -0.1838 0.033783 Total 5.595016 The standard deviation of x values (sx) can be found using MS-Excel. For that, type =STDEV.S(A2:A11) and hit enter, it gives 1.888562. Thus, sx = 1.888562 The number of observations are 10. So, n = 10 Now, putting all these values in the formula of test statistic, we get, P-value: It can be easily found using MS-Excel. Type =TDIST(13.465191, 8, 2) and hit enter. It gives 8.87E-07, that is, 8.87*10-7 Thus, p-value =0.000000887 Decision: Here, p-value is less than the level of significance, so we reject the null hypothesis. Conclusion: The slope of the regression line is not zero. At 5% level of significance, we conclude that the prediction is significant.