1) A realtor in Atlanta tells one of his clients that the average increase in th

Question

1) A realtor in Atlanta tells one of his clients that the average increase in the selling price of homes in Atlanta was $15,000 over the last year. The client thinks that the realtor must be overstating the true increase in prices. She takes a random sample of 100 houses and calculates a sample mean increase of $14,200. Assume that the standard deviation of the increase in the selling prices of homes in Atlanta is $5000. The client wants to do a statistical test of the realtor’s claim.

a) What should the client use for the null and alternative hypotheses?

b) What should her rejection region be for a test with = .1? What about = .05?

c) Specify the client’s test statistic and calculate its value.

d) Should the client reject the realtor’s claim at = .1? What about = .05?

e) What is the p-value of this test?

Explanation / Answer

Ho : miu = 15000

H1 miu is different from 15000

for alpha = 0.1 alpha / 2 = 0.05 critical values are : +/-1.64

for alpha = 0.05 alpha/2=0.025 critical values are +/- 1.96

Z= 14200 - 15000 / [ 5000 / srqt(100) ]

Z = -1.6

p value : 0.0548

for alpha = 0.1 we reject Ho

for alpha = 0.05 we fail to reject Ho

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