Advanced Hypothesis Testing

Advanced Hypothesis Testing

Team A:

Jennifer Ambrose

Jeffery Bruns

Paul Grove

Paul Miller

Brean Rossiter

RES 342

Alexander Heil

December 18, 2006

Advanced Hypothesis Testing

Statistical analysis has proved to be an essential tool towards gaining a better understanding of many business needs. Last week in John Smith's quest of moving his home based business into an office setting he compared the mean price from the Seattle Realtor Magazine to the price information from his sample of eight office buildings. Through a t-test statistical analysis John could not conclude that the price per-square-foot for the office space in Seattle is more than $17. However, before John moves out he decides to do a little more investigation based upon a sampling of 43 prices of office space he was able to collect. This week John will formulate a hypothesis statement and perform the five-step hypothesis test on the data he collected. After completing his analysis of the 43 prices, he will be able to compare the results from his t-test to the results from this analysis.

John Smith is running a financial planning business out of his home. His primary business tools are his experience, cell phone, laptop/PC, and the den in his home. John's clientele has grown large enough that he feels he is ready to move his home business into an office space. He read in Seattle Realtor Magazine that the mean price of leasing office space in Seattle is $17 per square foot, and that the standard deviation of the price per square foot is $2.15. If this is true, John believes he can afford to move out of his cramped den and into a new office space. John prices the listings of 43 office spaces in Seattle and found that the mean price per square foot for leasing office space to be $16.50. At the 0.05 significance level, John wants to determine if his experience is different from that claimed by Seattle Realtor Magazine. He will use the five-step hypothesis test he learned from his Research and Evaluation II course to determine the feasibility of his move. He dusts off his Statistical Techniques in Business and Economics book and gets to work.

Step 1: State the null hypothesis and the alternate hypothesis. John decides to formulate both a verbal and numerical hypothesis statement.

Verbal:

- Null hypothesis: The mean price per square foot for office space in Seattle is equal to $17.

- Alternate hypothesis: The mean price per square foot for office space in Seattle is not equal to $17.

Numerical:

- Null hypothesis:

- Alternate hypothesis:

Step 2: Select the level of significance.

John will be using the 0.05 level of significance.

Step 3: Select the test statistic.

John will be using the z-test statistic.

Step 4: Formulate the Decision Rule.

Since this is a two-tailed test, John uses .4750 (.5000 - .0250) to determine the critical values. The critical values of z are -1.96 and 1.96 (derived from Appendix D of Statistical Techniques in Business and Economics).

From this information John decides to reject the null hypothesis and accept the alternate hypothesis if the computed value of z is not between - 1.96 and 1.96. He will not reject the null hypothesis if z falls between - 1.96 and 1.96

Step 5: Make a decision and interpret the result.

The test statistic is - 1.52 obtained by:

Therefore, because - 1.52 is between - 1.96 and 1.96, John does not rejects the null hypothesis and accept the alternate hypothesis.

John determines that the probability of him finding a z value of 1.52 or more is 0.0643, found by 0.5000 - 0.4357 (derived from Appendix D of Statistical Techniques in Business and Economics). To compute the p-value, John needs to be concerned with the region less than - 1.52 and the region greater than 1.52. Since the rejection region is in both tails, John ascertains that the two-tailed p-value is 0.1286, found by 2(0.0643). The p-value