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	45	35
4	38	30
5	40	30
6	39	35
7	35	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 modelmean price for the standard model.)

H₀:

_d= 10

H_a:

_d10

H₀:

_d10

H_a:

_d> 10

H₀:

_d> 10

H_a:

_d10

H₀:

_d= 10

H_a:

_d10

H₀:

_d10

H_a:

_d= 10

Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate thep-value. (Round your answer to four decimal places.)p-value = State your conclusion.

RejectH₀. There is sufficient evidence to conclude that a $10 price differential exists.Do not RejectH₀. There is sufficient evidence to conclude that a $10 price differential exists. RejectH₀. There is insufficient evidence to conclude that a $10 price differential exists.Do not rejectH₀. 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. Usethe mean price for the deluxe modelthe mean price for the standard model.)$ to $