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.

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 = $220,000Sample mean, [tex]\bar{x}[/tex] = $210,000Sample size, n = 81Significance level, α = 0.051Population standard deviation, σ =  $36,000First, 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 .00621Since,  P-value < Significance levelWe reject the null hypothesis and accept the alternate hypothesis. Thus, there has been a significant decrease in the average price homes.