Question

Suppose that in past years the average purchase price per square foot for warehouse space in the United States has been $32.28. A national real estate investor wants to determine whether that figure has changed. The investor hires a researcher who randomly samples 19 warehouses that are for sale across the United States and finds that the mean is $32.73. The population standard deviation is $1.29. Can the researcher conclude that the average purchase price per square foot has changed? Test at the 90% confidence level.

1. State the null and alternative hypotheses.

2. Specify alpha based on the confidence level indicated.

3. Use alpha to develop the critical value that delineates the rejection region.

4. Compute the test statistic

5. Calculate P-value based on test statistic.

6. Compare the test statistic to the critical value. Compare the P-value to alpha.

7. Based on your comparisons identify your decision.

8. Indicate the conclusion for the scenario

Answer 1

1)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 32.28
Alternative Hypothesis, Ha: μ ≠ 32.28

2)
0.10 is alpha

3)

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645

4)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (32.73 - 32.28)/(1.29/sqrt(19))
z = 1.52

5)

P-value Approach
P-value = 0.1285

6)

1.52 < 1.645

As P-value >= 0.1,

7)

fail to reject null hypothesis.

8)

There is not sufficient evidence to conclude that figure has changed.