Checking Advertised Contents. A manufacturer of liquid detergent produces a bottle with an advertised content of 450 millilitres (mL). Fourteen bottles are randomly selected and found to have the following contents, in mL.

447 459 439 443 462 449 437 458 453 461 445 467 456 448 A normal probability plot of the data indicates that you can assume the contents are normally distributed. Let μ denote the mean content of all bottles produced. To decide whether the mean content is less than advertised, perform the hypothesis test H0: μ = 450 mL Ha: μ < 450 mL at the 10% significance level.

a. Use the t-test.

b. Use the Wilcoxon signed-rank test.

c. If the mean content is in fact less than 450 mL, how do you explain the discrepancy between the two tests?