A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. (a) The manufacturer's suggested retal prices for the two modeis show a $10 price differential. Use a 0,05 level of significance and test that the mean difference between the prices of the two models is $10. State the null and alternative hypotheses. (Use d= mean price for the deluxe model - mean price for the standard model.) H0:d10Ha:d>10H0:d>10Ha:d10H0:d=10Ha:d10H0:d=10Ha:d=10H0:d=10Ha:d=10 H0:d=10Ha:d=10H0:d=10Ha:d=10 Calculate the value of the test statistic. (Round your answer to three decimal places.) . Calculate the p-value. (Round your answer to four decimal places.) p-value=x State your conclusion. Reject H0. There is insufficient evidence to conclude that a $10 price differential exists. Do not reject H0. There is insufficient evidence to conclude that a $10 price differential exists. Reject H0. There is sufficient evidence to conclude that a $10 price differential exists. Do not Reject H0. There is sufficient evidence to conclude that a $10 price differential exists. (b) What is the 95% confidence interval for the difference between the mean prices of the two models (in dollars)? (Round your answers to nearest cent. Use the mean price for the deluxe model - the mean price for the standard model.) $to$