Question

Suppose that in past years the average price per square foot for warehouses in the United States has been $32.28. A national real estate investor wants to determine whether that figure has declined now. The investor hires a researcher who randomly samples 49 warehouses that are for sale across the United States and finds that the mean price per square foot is $31.67, with a sample standard deviation of $1.29. At 5% level of significance, test to see if the average price per square foot for warehouses in the U.S. has declined. Interpret your result

Answer 1

The provided sample mean is and the known population standard deviation is, and the sample size is n = 49

The following null and alternative hypotheses need to be tested:

Ho: μ=32.28

Ha: μ≠​32.28

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is

z_c​=1.96.

The z-statistic is computed as follows:

Since it is observed that ∣z∣=3.31>zc​=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0009, and since p=0.0009<0.05, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 32.28, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval is 31.309<μ<32.031.

The critical value of z is - 1.96 and +1.96.
The critical value is z = ± 1.96 for a two-tailed test at 5% level of significance. Since, the computed value of z= -2.1 falls in rejection region, we reject the null hypothesis. Hence, the average price per square foot for warehouses has changed now.