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.

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, = $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

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

Formula:

Putting all the values, we have

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.