Practical vs. Statistical Significance on Tax Issues. A start-up company has developed a new software to help users file U.S. income taxes. They have priced their product at $89.99 (compared to only $58 for Premium TaxAct online, for example, which is one of the established tax products on the market.) Tax software licenses are only valid for the year in which they are purchased, so customers using either of these services would need to pay each time they file their taxes. The argument for the higher price of the start-up company's software is that their product increases tax returns over any of the competitors' products. To check this claim using TaxAct as the reference product, a customer service agency collected data from a large randomly selected sample of customers filing taxes with the new software, and obtained a sample mean increase in the tax return (when compared to TaxAct) of $15 dollars. That is, customers using the new software saved on average $15 more than they would have using TaxAct. The agency finds that the p-value associated with the one-sided hypothesis test, assuming that the mean increase in the tax return (when compared to TaxAct) is $0, is p = 0.005. (a) Based on this p-value, there is... little to no evidence against the null hypothesis. borderline/weak evidence against the null hypothesis. moderate evidence against the null hypothesis. substantial/strong evidence against the null hypothesis. extremely strong/overwhelming evidence against the null hypothesis. (b) Would you say that the results are practically meaningful, i.e., is it worth buying the new product? No, because the difference in tax returns is, on average, less than the difference in the price paid for the more expensive product. Yes, because the difference in tax returns is, on average, less than the difference in the price paid for the more expensive product. No, because the p-value doesn't indicate a statistical difference. Yes, because the p-value indicates a statistical difference. 6. Answer the following True/False Questions (a) All else remaining equal (i.e., keeping the sample mean x and the sample standard deviation s constant), increasing sample size, n, leads to stronger evidence against the null hypothesis. (b) A p-value of .10 is stronger evidence against the null hypothesis than a p-value of .01. (c) The decision to use a one-sided or two-sided test is usually made before the data are analyzed. (d) If the sample mean is known, there is no need to test hypotheses concerning the population mean.