You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople just returned to the office with a newly designed advertisement. The average cost per square foot of home sales based on this advertisement is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280. In other words, he claims that the newly designed advertisement would result in higher average cost per square foot in the Pacific Region. He wants you to make sure he can make that statement before approving the use of the advertisement. In order to test his claim, you will generate a random sample size of 750 using data for the Pacific region and use this data to perform a hypothesis test.
Generate a sample of size 750 using data for the Pacific region. Then, design a hypothesis test and interpret the results using significance level α = .05. You will work with this sample in the assignment. Briefly describe how you generated your random sample.
- Hypothesis Test Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test.
- Define your population parameter.
- Write the null and alternative hypotheses. Note: Remember, the salesperson believes that his sales are higher.
- Specify the name of the test you will use.
- Identify whether it is a left-tailed, right-tailed, or two-tailed test.
- Identify your significance level.
- Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and find the test statistic and significance level.
- Provide the descriptive statistics (sample size, mean, median, and standard deviation).
- Provide a histogram of your sample.
- Describe your sample by writing a sentence describing the shape, center, and spread of your sample.
- Determine whether the conditions to perform your identified test have been met.
- Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis.
- Calculate the sample mean and standard error.
- Determine the appropriate test statistic, then calculate the test statistic.
Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean (Pacific), and the target is 280.
- Calculate the p value.
Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size.
Choose your test from the following:
=T.DIST.RT([test statistic], [degree of freedom])
=T.DIST([test statistic], [degree of freedom], 1)
=T.DIST.2T([test statistic], [degree of freedom])
- Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.
- Test Decision: Discuss the relationship between the p value and the significance level, including a comparison between the two, and decide to reject or fail to reject the null hypothesis.
- Discuss how the p value relates to the significance level.
- Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis.
- Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance.
- Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.