FinalProjectMilestone2_AyeshabiTigdikar_20230617

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Final Project – Milestone 2 Probability Theory & Introductory Statistics Ayeshabi W Tigdikar Master of Science in Project Management, Northeastern University Professor Tom Breur June 17 th , 2023

T ABLE OF C ONTENTS O RIGINAL Q UESTIONS ............................................................................................................................ 2 H YPOTHESIS T ESTING ............................................................................................................................. 3 R ESULTS .................................................................................................................................................... 3 R EFERENCES ............................................................................................................................................. 5 A PPENDIX .................................................................................................................................................. 6

O RIGINAL Q UESTIONS The questions identified in part 1 were, 1. "What are the highest and lowest retail stores by county?" 2. "What are the highest retail stores by city?" 3. "What are the highest establishments?" 4. “Which city has the highest square footage?” H YPOTHESIS T ESTING Given that the stores in Bronx and the stores in New York counties represent two distinct populations, we performed a two-sample t-test to compare the average square footage for the two cities. The means of two distinct populations are compared using a two-sample t-test. The Bronx and the counties of New York constitute the two autonomous populations in this instance. We also have the option of using a paired t-test, but this is only appropriate when there are two dependent populations. Because the stores in the Bronx and the stores in the Erie counties are different, the two populations are not dependent on one another in this instance. We conduct a one-sample t-test to determine whether the average square footage of stores in New York is 15000 square feet since we are only interested in comparing the average square footage of convenience and bakery stores in New York to a single value, 15000 square feet. When comparing a single population's mean to a predetermined value, a one-sample t-test is employed. In this instance, the only population is comprised of the shops in New York, and the known value is 15,000 square feet. The steps for performing a one / two-sample t-test are as follows: 1. List the null and alternative hypotheses. 2. Decide on a significance level: The likelihood of denying the null hypothesis when it is true is known as a significance level. The significance level of 0.05 is usual. 3. Determine the t-statistic and p-value: The t-statistic calculates the difference between the two means. If the null hypothesis is correct, the p-value is the likelihood that a t-statistic as extreme as the one you observed would be obtained. 4. Decide: You can reject the null hypothesis if the p-value is less than the significance level. R ESULTS Two questions that can be addressed using inferential statistics and hypothesis testing are: 1. Is there a significant difference in the average square footage of stores in Bronx and New York? (Two sample T Test)

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Hypothesis:  Null Hypothesis (H0): The actual difference in square footage between stores in the Bronx and those in New York is zero.  Alternative Hypothesis (HA): The actual difference between Bronx and New York retail stores average square footage is not equal to zero. Observations:  The test's computed t-value is -3.197.  The t-test has a degree of freedom (df) of roughly 1086.3.  The test's p-value is 0.001429, which is below the 0.05 threshold for significance.  We have enough data from the outcomes to rule out the null hypothesis. As a result, we can draw the conclusion that the mean square footage of stores in the Bronx and New York differs significantly.  The computed 95% confidence interval for the mean difference is (-1577.1409, -377.4942). The genuine difference in means of square footage therefore resides within this range, with a 95% confidence level.  Additionally, the sample estimate for the mean square footage of stores in the Bronx is 1955.277, whereas the sample estimate for stores in New York is 2932.594.  These findings point to a statistically significant difference in the amount of square footage between Bronx and New York stores, with New York stores typically having more space than Bronx stores. 2. Do convenience and bakery stores in New York State have an average square footage of more than 15,000 square feet? (One sample T test)

Hypothesis:  Null Hypothesis (H0): The true mean of the Square Footage in the population is equal to 15,000.  Alternative Hypothesis (HA): The true mean of the Square Footage variable in the population is not equal to 15,000. Observation:  The test's computed t-value is -0.26092  The t-test has a degree of freedom (df) of roughly 44.  The test's p-value is 0.7954, which is above the 0.05 threshold for significance.  The alternative hypothesis states that the true mean is not equal to 15,000. The 95 percent confidence interval for the mean is (8563.567, 19960.877).  The sample estimate for the mean of the square ft is 14,262.22.  Based on these results, since the p-value (0.7954) is greater than the significance level (commonly set at 0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the true mean of the convenience and bakery stores in New York is different from 15,000. In the first analysis, we used a two-sample t-test to compare the typical square footage of retailers in the Bronx and New York. The alternative hypothesis proposed a non-zero difference, whereas the null hypothesis claimed there is no actual difference in square footage between the two places. The data showed a considerable difference in the average square footage between the Bronx and New York retailers, which offered solid evidence to support the alternative hypothesis. In comparison to retailers in New York, the average square footage in the Bronx was determined to be smaller, with a 95% confidence interval of -1577.1409 to -377.4942. These studies show how different places' stores come in a variety of sizes, which may be influenced by variables like space constraints or consumer preferences. In the second analysis, we used a one-sample t-test to look at the typical square footage of convenience and bakery businesses in New York State. The alternative hypothesis suggested a departure from the null hypothesis' assumption that the actual mean square footage of these stores is equal to 15,000 square feet. The findings indicate that there is no significant difference in the average square footage compared to the presumptive value of 15,000 square feet, but there is insufficient evidence to reject the null

hypothesis. With a 95% confidence interval ranging from 8,563.567 to 19,960.877, the estimated average square footage for convenience and bakery businesses in New York State is 14,262.22. R EFERENCES Retail Food Stores . Data Catalog. (2023, February 24). https://catalog.data.gov/dataset/retail- food-stores Retail Food Stores: State of New York . Retail Food Stores | State of New York. (2023, February 13). https://data.ny.gov/Economic-Development/Retail-Food-Stores/9a8c-vfzj A PPENDIX

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