Question

The Carpet Corner in Gladstone, Missouri, offers a variety of carpets, wood flooring, and tiles. Sales records indicate that the mean amount of carpet installed in a wall-to-wall carpeted residential home by crews from this store is 1,250 square feet. The store manager, Frank Vida, believes that when there is a sale, customers translate the savings into carpeting a larger area. A random sample of 45 wall-to-wall carpet purchases was selected during a sale. The sample mean was x = 1,304 square feet. Assume that σ = 155 square feet.

(a) Conduct a one-sided, right-tailed test of H0: μ = 1,250 versus Ha: μ > 1,250. Is there any evidence to suggest the true mean square footage is larger during a sale?

Use α = 0.01.

Calculate the test statistic. (Round your answer to four decimal places.)

z= ______________________

Find the probability of a Type II error if the true mean square footage during a sale is

μ_a = 1,330;  that is,

find β(1,330). (Round your answer to four decimal places)

β(1,330) = __________________

Answer 1

a)

population mean μ=	1250
sample mean 'x̄=	1304.000
sample size    n=	45.00
std deviation σ=	155.000
std error ='σx=σ/√n=	23.1060
test stat z = '(x̄-μ)*√n/σ=	2.3371

rejection region: Xbar >=μ+Zα*σx or Xbar>=	1303.7527
rejection region: Xbar >=			1303.753

P(Type II error) =P(Xbar<1303.753|μ=1330)=P(Z<(1303.7527-1330)/23.106)=P(Z<-1.14)=

0.1271

P(β) =P(Xbar<1303.753|μ=1330)=P(Z<(1303.7527-1330)/23.106)=P(Z<-1.14)=

0.1280