Question

The average house proce in Lincoln Park based on the random sample of 64 homes is $525,000. Your friend at the Chicago City Office tells you that the standard deviation of the house prices based on all houses in Lincoln Park is $80,000. An outside expert tells you that she believes that the average house price of a house in Lincoln Park is $515,000. Do you reject the hypothesis that the average house price is $515,000, Vs. alternative that it is not (two-sided)? Your boss tells you that the alpha is 10%.

Answer 1

Let the random variable X represent the average price of house in Lincoln Park.

Null Hypothesis :

Alternative Hypothesis :

We will test this hypothesis at 10% significance level.

The standard error would be given by,

The test statistic would be given by,

The p-value corresponding to 1.00 standard score is 0.3174. Since the p-value is greater than significance level we do not reject the null hypothesis. Therefore the evidence suggest that average house is $515,000 at 10% significance level.