You may need to use the appropriate technology to answer this question.

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.

Retail Outlet	Model Price ($)
Deluxe	Standard
1	39	27
2	39	28
3	44	36
4	38	30
5	40	30
6	39	34
7	34	29

(a)The manufacturer's suggested retail prices for the two models 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:_d = 10

H_a:_d 10

H₀:_d 10

H_a:_d > 10

H₀:_d > 10

H_a:_d 10

H₀:_d = 10

H_a:_d 10

H₀:_d 10

H_a:_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 = ________________

State your conclusion.

• Do not Reject H₀. There is sufficient 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 insufficient evidence to conclude that a $10 price differential exists.
• Reject H₀. There is insufficient 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 $ _____________