Prompt
Generate a sample of size 750 houses using data for the Pacific region. Then, design a hypothesis test and interpret the results using significance level $a=.05$. You will work with this sample in this assignment. Briefly describe how you generated your random sample.
Use the House Listing Price by Region Yjocument to help support your work on this assignment. You may also use the Descriptive Statistics in Excel PDF and Creating Histograms in Excel PDF tutorials for support.
Specifically, you must address the following rubric criteria, using the Module Five Assignment Template Word Document
- Introduction: Describe the purpose of this analysis and how you generated your random sample size of 750 houses.
- 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.
- Specify the name of the test you will use.
- Identify whether it is a left-tailed, right-tailed, or two-tailed test.
- Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and identify the test significance level.
- Provide the descriptive statistics (sample size, mean, median, and standard deviation).
- Provide a histogram of your sample.
- Summarize your sample by writing a sentence describing the shape, center, and spread of your sample.
- Check whether the assumptions to perform your identified test have been met.
- Identify the test significance level. For example, $a=.05$.
- 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.

Step 1 ：Generate a random sample of 750 houses from the Pacific region data. This can be done using a random sampling method.

Step 2 ：Define the population parameter. In this case, the population parameter is the mean house price in the Pacific region.

Step 3 ：Write the null and alternative hypotheses. The null hypothesis is that the mean house price in the Pacific region is equal to a specified value, and the alternative hypothesis is that the mean house price is not equal to that value.

Step 4 ：Specify the name of the test to be used. In this case, a t-test will be used.

Step 5 ：Identify whether it is a left-tailed, right-tailed, or two-tailed test. This will be a two-tailed test as we are looking for a difference in either direction from the specified value.

Step 6 ：Provide the descriptive statistics for the sample, including the sample size, mean, median, and standard deviation.

Step 7 ：Provide a histogram of the sample data. This will give a visual representation of the distribution of house prices in the sample.

Step 8 ：Summarize the sample by describing the shape, center, and spread of the data.

Step 9 ：Check whether the assumptions to perform the t-test have been met. These assumptions include that the data is normally distributed and that the sample is randomly selected and independent.

Step 10 ：Identify the test significance level. In this case, the significance level is \(\alpha = 0.05\).

Step 11 ：Calculate the sample mean and standard error. The standard error can be calculated as the standard deviation divided by the square root of the sample size.

Step 12 ：Determine the appropriate test statistic. This can be calculated as (mean - target)/standard error. In this case, the target is 280.

Step 13 ：Calculate the p-value. This is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Step 14 ：Compare the p-value to the significance level. If the p-value is less than the significance level, reject the null hypothesis. If the p-value is greater than the significance level, fail to reject the null hypothesis.

Step 15 ：Interpret the results. If the null hypothesis was rejected, conclude that the mean house price in the Pacific region is not equal to the specified value. If the null hypothesis was not rejected, conclude that the data does not provide strong evidence that the mean house price is different from the specified value.