Mr. James McWhinney, president of Daniel-James Financial Services, believes ther

Question

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The x column indicates the number of client contacts last month and the Y column shows the value of sales ($ thousands) last month for each client sampled. (Round your answers to 3 decimal places.) Number of Contacts, X Sales ($ thousands), Y Number of Contacts, X Sales ($ thousands), Y 14 24 23 30 12 14 48 90 20 28 50 85 16 30 55 120 46 80 50 110 PictureClick here for the Excel Data File a. Determine the .95 confidence interval, in thousands of dollars, for the mean of all sales personnel who make 40 contacts. [ , ] b. Determine the .95 prediction interval, in thousands of dollars, for a particular salesperson who makes 40 contacts. [ , ]

Explanation / Answer

(a) The 95% confidence interval is [55.165, 84.308]

(b) The 95% prediction interval is [22.793, 116.680]

Regression Analysis r² 0.790 n   10 r   0.889 k   1 Std. Error   19.351 Dep. Var. Y ANOVA table Source SS   df   MS F p-value Regression 11,253.0837 1   11,253.0837 30.05 .0006 Residual 2,995.8163 8   374.4770 Total 14,248.9000 9   Regression output confidence interval variables coefficients std. error    t (df=8) p-value 95% lower 95% upper std. coeff. Intercept -16.6266 0.000 X 2.1591 0.3939 5.482 .0006 1.2508 3.0673 0.889 Predicted values for: Y 95% Confidence Interval 95% Prediction Interval X Predicted lower upper lower upper Leverage 40 69.736 55.165 84.308 22.793 116.680 0.107

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