5-3 rough draft

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Southern New Hampshire University *

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MAT240

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Marketing

Date

Feb 20, 2024

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docx

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Uploaded by LieutenantElephantMaster868

Introduction [Describe the purpose of this analysis. Briefly describe how you generated your random sample of 750 houses (ie: =rand()).] Introduction The objective of this analysis is to verify a statement put forward by the marketing director regarding the newly designed advertisement. According to the claim, the advertisement is expected to lead to a higher average cost per square foot in the Pacific Region. To investigate this claim, we will generate a random sample of 750 houses using data from the Pacific region. This sample size was carefully selected using Excel function =RAND() sorted smallest to largest to ensure it is representative of the population and guarantees the accuracy of our findings. Hypothesis Test Setup [Define your population parameter.] [Write the null and alternative hypotheses.] [Specify the name of the test you will use and identify whether it is a left-tailed, right-tailed, or two- tailed test.] Hypothesis Test Setup Our focus lies on the population parameter, specifically the average cost per square foot for all homes in the Pacific Region. Null Hypothesis: The average cost per square foot for homes in the Pacific Region equals $280. Alternative Hypothesis: The average cost per square foot for homes in the Pacific Region is less than $280. To assess whether our data provides substantial evidence to reject the null hypothesis, we will employ a left-tailed t-test. This test exclusively evaluates if the average cost per square foot is less than $280, disregarding the possibility of it being greater or equal. Data Analysis Preparations [Provide the descriptive statistics of the sample (sample size, mean, median, and standard deviation).] [Provide a histogram of the 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, α = .05] Data Analysis Preparations

To conduct my hypothesis test, I will use the data from the House Listing Price by Region Excel document. Specifically, I will focus on the Pacific Region, which comprises a sample of 750 homes. Let me provide you with the descriptive statistics for our sample: Descriptive Sample Statistics: Mean: 260 Median: 199 Standard Deviation: 155 Sample Size: 750 . Based on the histogram, it is evident that the data is skewed to the right, indicating a non-normal distribution. The central tendency of the data appears to be around 200, with a spread of approximately 155. This suggests a significant variability in the prices per square foot for homes in the Pacific Region. To conduct our left-tailed t-test, we assume that the data follows a normal distribution and that the sample was randomly selected from the population. Furthermore, we assume equal variances between groups. Our chosen level of significance (α) for the test is set at .05. This means that if the calculated p-value is less than .05, we can reject the null hypothesis. Calculations [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 using one of the following tests:] Excel Function Type of Test Right-tailed =T.DIST.RT([test statistic], [degree of freedom]) Left-tailed =T.DIST([test statistic], [degree of freedom], 1) Two-tailed =T.DIST.2T([test statistic], [degree of freedom]) [Note: The degree of freedom is calculated by subtracting 1 from your sample size.] [Use the normal curve graph as a reference to describe where the p value and test statistic would be placed.] Calculations The Pacific Region's sample mean is 260, with a standard error calculated by dividing the population standard deviation (155) by the square root of our sample size (750), yielding a value of approximately 5.6.

Our test statistic follows the formula (mean – target)/standard error, resulting in (260 - 280)/5.6 = -3.57 in this case. By utilizing the T.DIST function in Excel, we can compute the p-value for our left-tailed test as follows: `=T.DIST(-3.57,749,1)` This computation yields a value of 0.000207426, which is smaller than our chosen significance level of .05. On the normal curve graph, our test statistic (-3.57) would be positioned to the left of the target value (280). The shaded area under the curve to the left of our test statistic represents the p-value. Test Decision [Compare the relationship between the p value and significance level.] [Decide to reject or fail to reject the null hypothesis.] Test Decision The obtained p-value (0.000207426) is smaller than the predetermined significance level of 0.05. This indicates a significant difference between the sample mean and the hypothesized population parameter. As a result, we reject the null hypothesis stating that the average cost per square foot for homes in the Pacific Region is equal to $280. Our findings strongly support the alternative hypothesis, indicating that there is ample evidence to suggest that the new advertisement will lead to a higher average cost per square foot in the region. 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. Conclusion Our test results validate our hypothesis, demonstrating that the average cost per square foot for homes in the Pacific Region is below $280. This discovery holds statistical significance, with a p-value well below our chosen threshold of .05. Furthermore, our comprehensive sample data and meticulous t-test calculations allow us to confidently assert that the Pacific Region exhibits a higher average cost per square foot, providing substantial support for our alternative hypothesis. These valuable insights will greatly inform our advertising efforts, as our forthcoming marketing campaign is poised to have a positive impact on home prices in this region. In summary, these statistically significant findings strongly support our initial hypothesis while elevating the overall quality of our analysis.

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5-3 rough draft

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