Question

a personal fitness produces both a deluxe and a standard model of a smoothie blender for home use. selling prices obtained from a sample of retail outlets follow. excel file: data10-27.xlsx model price ($) model price ($) retail outlet deluxe standard retail outlet deluxe standard 1 39 27 5 40 30 2 39 28 6 39 34 3 45 35 7 35 29 4 38 30 round your answers to 2 decimal places. a. the manufacturer's suggested retail prices for the two models show a price differential. use a level of significance and test that the mean difference between the prices of the two models is . - select your answer - b. what is the confidence interval for the difference between the mean prices of the two models?

Answer 1

To test the claim that the mean difference between the prices of the deluxe and standard models is zero, conduct a hypothesis test using the given sample data and assume the prices are normally distributed. Use a two-sample t-test with a significance level of 0.05 to determine if there is a significant mean difference between the prices of the two models. Calculate the confidence interval for the difference between the mean prices using the formula: CI = (x1 - x2) ± t * SE, where x1 and x2 are the sample means, t is the critical t-value, and SE is the standard error of the difference.

Step-by-step explanation:

To test the claim that the mean difference between the prices of the deluxe and standard models is zero, we will conduct a hypothesis test using the given sample data. We will assume that the prices of the two models are normally distributed and have equal variances.

a. To test the null hypothesis that the mean difference is zero, we will use a two-sample t-test. The significance level will be set at 5% (0.05). We will calculate the t-value and compare it to the critical value from the t-distribution with degrees of freedom equal to n1 + n2 - 2 (where n1 and n2 are the sample sizes for the deluxe and standard models, respectively). If the calculated t-value exceeds the critical value, we will reject the null hypothesis and conclude that there is a significant mean difference between the prices of the two models.

b. To calculate the confidence interval for the difference between the mean prices, we will use the formula: CI = (x1 - x2) ± t * SE, where x1 and x2 are the sample means for the deluxe and standard models, t is the critical t-value for the desired confidence level, and SE is the standard error of the difference. The standard error can be calculated as: SE = sqrt((s1^2 / n1) + (s2^2 / n2)), where s1 and s2 are the sample standard deviations for the deluxe and standard models, and n1 and n2 are the sample sizes. We will use t-values corresponding to the desired confidence level to calculate the confidence interval.