A national survey found that the average cost of a group of hand tools at Home D

Question

A national survey found that the average cost of a group of hand tools at Home Depot is 26.94. Sara found her average(through her own survey) to be 24.25 with a stdev of 5.87. She believes that the average cost of the group of tools is really LOWER than the national survey. Use a sample size of 9 tools. Test her claim at the 90% confidence level:

A. Choose the appropriate H1?

B. Choose the appropriate H0?

C. Choose the appropriate claim?

D. State the critical value/s?

E. State the test value/s?

F. What is the decision? (reject H0, reject H1, Reject both, reject neither, or none of these. )

G. Choose the correct conclusion? (Sara is correct, the cost is lower or Sara is correct, the cost is higher.

Explanation / Answer

Given:

Xbar = 24.25

S = 5.87

N = 9

Degrees of Freedom = n-1 = 8

Assumption : We assume that the data is normally distributed

a)

H1: µ < 26.94

b)

H0 : µ = 26.94

c)

Alpha = .1

d)

Tcritical = 1.398

e)

t = (Xbar - µ)/Sqrt(s2/n) = (24.25 – 26.94)/sqrt (5.872/9) = -1.375

f)

Pvalue = Tdist(1.375,8,1) = .897

Since Pvalue > .1, we fail to reject the null hypothesis

g)

Sara is incorrect, the cost is not less than 26.94.

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