Problem 8: 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.

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Problem 8:
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.
Transcribed Image Text:Problem 8: 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.
For these problems you should complete the 8 steps of the hypothesis testing process.
State the null and alternative hypotheses.
Specify alpha (a) based on the confidence level indicated.
Use alpha to develop the critical value that delineates the rejection region. Remember to use a/2
for two-tailed tests. Draw the curve and indicate the rejection region.
Use information from the problem to compute the test statistic
Calculate P-value based on test statistic.
1.
2.
3.
4.
5.
a) If population standard deviation or proportion use Z or normal distribution table
One tail: 0.5 – area in non cum table.
Two tailed: PV = 2* (0.5- area in non cum table)
b) If sample standard deviation use t table with df = n-1.
PV will be a range..e.g. 0.025 to 0.05.
Compare the test statistic to the critical value. Compare the P-value to alpha.
Based on your comparisons identify your decision (i.e. reject null hypothesis Ho or fail to reject
null hypothesis Ho). Reject the null hypothesis if the test statistic is in the rejection region.
Reject the null hypothesis if the P-value is smaller than alpha. The outcome of the p-value and
critical value approach will always lead to the same decision.
Indicate the conclusion for the scenario
6.
7.
8.
IF Reject Ho: at % (confidence level indicated) can conclude Ha
IF Fail to Reject Ho: at % (confidence level indicated) can NOT conclude Ha
Transcribed Image Text:For these problems you should complete the 8 steps of the hypothesis testing process. State the null and alternative hypotheses. Specify alpha (a) based on the confidence level indicated. Use alpha to develop the critical value that delineates the rejection region. Remember to use a/2 for two-tailed tests. Draw the curve and indicate the rejection region. Use information from the problem to compute the test statistic Calculate P-value based on test statistic. 1. 2. 3. 4. 5. a) If population standard deviation or proportion use Z or normal distribution table One tail: 0.5 – area in non cum table. Two tailed: PV = 2* (0.5- area in non cum table) b) If sample standard deviation use t table with df = n-1. PV will be a range..e.g. 0.025 to 0.05. Compare the test statistic to the critical value. Compare the P-value to alpha. Based on your comparisons identify your decision (i.e. reject null hypothesis Ho or fail to reject null hypothesis Ho). Reject the null hypothesis if the test statistic is in the rejection region. Reject the null hypothesis if the P-value is smaller than alpha. The outcome of the p-value and critical value approach will always lead to the same decision. Indicate the conclusion for the scenario 6. 7. 8. IF Reject Ho: at % (confidence level indicated) can conclude Ha IF Fail to Reject Ho: at % (confidence level indicated) can NOT conclude Ha
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