the mean price of houses in the us is $383,500. a real estate agent believes the mean price of houses in a…

the mean price of houses in the us is $383,500. a real estate agent believes the mean price of houses in a local neighborhood is less than the national mean. the agent takes a random sample of 30 houses and finds the mean price to be $295,089 with a standard deviation of $156,321. the real estate agent conducts a significance test with the alpha level $alpha = 0.05$ for the mean price of houses in the neighborhood being less than $383,500. the p - value for this significance test is 0.002. what is the correct interpretation of the p - value?\nassuming the true mean price of houses is $383,500, there is a 0.2% probability that the null hypothesis is true by chance alone.\nassuming the true mean price of houses is $383,500, there is a 0.2% probability of getting a sample mean of $295,089 by chance alone.\nassuming the true mean price of houses is $383,500, there is a 0.2% probability of getting a sample mean at least as extreme as $295,089 by chance alone.\nassuming the true mean price of houses is $383,500, there is a 99.8% probability that a sample mean of $295,089 or greater will occur by chance alone.

the mean price of houses in the us is $383,500. a real estate agent believes the mean price of houses in a local neighborhood is less than the national mean. the agent takes a random sample of 30 houses and finds the mean price to be $295,089 with a standard deviation of $156,321. the real estate agent conducts a significance test with the alpha level $alpha = 0.05$ for the mean price of houses in the neighborhood being less than $383,500. the p - value for this significance test is 0.002. what is the correct interpretation of the p - value?\nassuming the true mean price of houses is $383,500, there is a 0.2% probability that the null hypothesis is true by chance alone.\nassuming the true mean price of houses is $383,500, there is a 0.2% probability of getting a sample mean of $295,089 by chance alone.\nassuming the true mean price of houses is $383,500, there is a 0.2% probability of getting a sample mean at least as extreme as $295,089 by chance alone.\nassuming the true mean price of houses is $383,500, there is a 99.8% probability that a sample mean of $295,089 or greater will occur by chance alone.

Answer

Answer:

Assuming the true mean price of houses is $383,500, there is a 0.2% probability of getting a sample mean at least as extreme as $295,089 by chance alone.

Brief Explanations:

The P - value is the probability of obtaining a sample result as extreme or more extreme than the one observed, assuming the null hypothesis (true mean is $383,500 here) is true. A lower P - value provides evidence against the null hypothesis.