The average price of homes sold in the US in the past year w

The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. At 95% confidence test to determine if there has been a significant decrease in the average price homes.

a.

State the null and alternative hypotheses to be tested.

b.

Compute the test statistic.

c.

Determine the critical value for this test.

d.

What do you conclude?

e.

Compute the p-value.

Solution

(a) Let mu be the population mean

Null hypothesis: mu=220,000

Alternative hypothesis: mu<220,000

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(b)test statistic:

Z=(xbar-mu)/(s/vn)

=(210000-220000)/(36000/sqrt(81))

=-2.5

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(c) It is a left-tailed test.

Given a=1-0.95=0.05, the critical value is Z(0.05) = -1.645 (from standard normal table)

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(d) Since Z=-2.5 is less than -1.645, we reject the null hypothesis.

So we can conclude that there has been a significant decrease in the average price homes.

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(e)p-value = P(Z<-2.5) =0.0062 (from standard normal table)