Data are available for 542 dishwashers (see http://www.quietestdishwashers.com/m

Question

Data are available for 542 dishwashers (see http://www.quietestdishwashers.com/most-viewed/ ). For each dishwasher, two numbers are available: the “noise rating” of the dishwasher, measured id dB, and the price of the dishwasher in dollars.

Suppose a researcher decides to use noise rating to predict ln(price) instead of price. Some computer output is given below:

3. What is a 95% confidence interval for the price of a dishwasher that made no noise (0 dB)?

A. 3394 to 3732

B. -54.0 to -47.7

C. 9.90 to 10.30

D. -0.0685 to -0.0611

E. 19,921 to 29,666

1 SUMMARY OUTPUT Regression Statistics 4 Multiple R 5 R Square 6 Adjusted R Square0.686431146 7 Standard Error 8 Observations 9 10 ANOVA 0.82886112 0.687010756 0.258525304 542 12 Regression 13 Residual 14 Total 15 16 17 Intercept 18 rating 1 79.21984662 36.0910797 541115.3109263 540 Coefficients Standard Error 10.09864687 0.101360651 -0.0647632280.001881112

Explanation / Answer

3. What is a 95% confidence interval for the price of a dishwasher that made no noise (0 dB)?

So at no noise, the predicted value of price of dishwater will be the intercept.

Here 95% confidence value of intercept = a +- t541,0.05 (sea)

= 10.09865 +- 1.96436 * 0.10136

= (9.90, 10.30)

Now the given data is logarithmic. So taking exponential both side.

Lower bound = exp(9.90) = 19921

Upper BOund = Exp(10.30) = 29666

so OPtion E is correct.

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