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 a sample mean price of $210,000. It is known that the standard deviation of the population is $36,000. Using a 1% level of significance, test to determine if there has been a significant decrease in the average price homes. Use the p value approach. Make sure to show all parts of the test, including hypotheses, test statistic, decision rule, decision and conclusion.

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ChiKesselman ChiKesselman · Answer 1 · 2019-12-04T07:50:12+01:00

Answer:

We conclude that there has been a significant decrease in the average price homes.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $220,000

Sample mean, [tex]\bar{x}[/tex] = $210,000

Sample size, n = 81

Significance level, α = 0.051

Population standard deviation, σ = $36,000

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 220000\text{ dollars}\\H_A: \mu < 210000\text{ dollars}[/tex]

We use One-tailed z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{210000 - 220000}{\frac{36000}{\sqrt{81}} } = -2.5[/tex]

Calculating the p-value from the z-table, we have:

P-value = 0 .00621

Since,

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, there has been a significant decrease in the average price homes.