Introduction St. Louis community college Sustainability committee has been contracted for a study concerning possible food deserts within the St. Louis metropolitan area. In order to do this, one thousand samples of the metropolitan areas will be taken from the St. Louis white pages and Google maps will be used to determine the distance from the addresses to a market. A market is considered to be a store that includes fresh food, vegetables, fruits, and chicken. With some samples it was difficult to make this decision. For example convenience, thrift stores, and food stands were not considered to meet these criteria.
A team of four members were put together to formulate this report. The recorder was Alicia Witzofsky and the facilitator was Lisa Manis. Each member of the team collected 250 samples from the St. Louis metropolitan area. These samples were compiled into an Excel spreadsheet. The collected data included the individuals name, address, city, zip-code, and distance to the closest market. This data is included in appendix.
Null Hypothesis and Alternative Hypothesis
The null hypothesis, H0: μ ≤ 1.5 was chosen based on the client’s specifications. If the individuals address is not located within 1.5 mile of a market, that persons’ address is considered to be within a food desert. Similarly, the alternative hypothesis, H1 μ > 1.5, is that the average distance is greater than 1.5 miles and is within a food desert.
Level of Significance The level of significance was chosen based on the decision to accept 95% accuracy of the information, meaning that if all possible samples are taken and confidence intervals are developed, 95% of them would include the true population mean somewhere within their interval. We are saying that we have 95% confidence that we have selected a sample whose interval does include the population mean. There is a risk of committing an error when the calculations are incorrect. A type I error occurs if you reject the null hypothesis, H0, when it is true and should not be rejected. The probability of a type I error occurring is α (alpha), 0.05. A type II error occurs if you do not reject the null hypothesis, H0, when it is false and should be rejected. The probability of a type II error occurring is β (beta).
Sample Size The number of samples 1000 was chosen when the probabilities of type I and type II errors occurring were considered. Each person in the group collected 250 samples. From the 1000 samples 79 samples were pulled from Ballwin and 92 samples were pulled from Florissant because they offered a diverse comparison of samples. A type I error would occur if we reject that the average distance from an address to a market is less than or equal to 1.5 miles even though it is in fact less than or equal to 1.5 miles. A type II error occurs when we accept that the average distance from an address to a market is less than or equal to 1.5 when it is actually greater than the 1.5 miles from the market. If these errors occur than we would be going over budget constraints in order to get the correct information and calculations.
For the clients sake we decided to do two tests and they are the T-STAT test and the Confidence Interval test. Since the standard deviation for the population is unknown we have to use T-STAT test. The reason we also decided to do Confidence Interval is because we want to match our results and be confident. Also, in order to solve T-STAT test and Confidence Interval test we need to solve Sample Pooled Variance too. We were able to use the Sample Pooled Variance formula because we were able to make the assumptions that the populations are normally distributed with equal variances and the means of both populations are also equal and independent.
We determined that a one…