Food deserts have become a particularly hot topic in the public health community as anexplanation for a variety of negative health outcomes in disadvantaged areas. Aresearcher is interested in comparing the average shelf space provided by supermarkets,convenience stores, and corner stores in two different communities in order to address thegrowing concern for food deserts. Assume the following table reports the summary statistics for shelf space dedicated to fresh fruits and vegetables (meters) obtained from SRSs of a variety of different stores that supply groceries from each community. Community Average Shelf Space For Fruits and Veg. (m) Sample Standard Deviation Sample Size "Food Desert" 13.7 2.4 12 Other Community 89.4 14.6 14 a) Carry out the appropriate statistical test in order to determine if there is a significant difference in mean shelf space between the two communities at the alpha level of 0.05. Assume all conditions for the test are met. Do not assume equal variances. Write out your null and alternative hypotheses, and correctly interpret your p-value. b) Construct a 95% confidence interval for your estimate for the average difference in shelfspace provided for fresh fruits and vegetables. Provide an interpretation for your interval.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Food deserts have become a particularly hot topic in the public health community as anexplanation for a variety of negative health outcomes in disadvantaged areas. Aresearcher is interested in comparing the average shelf space provided by supermarkets,convenience stores, and corner stores in two different communities in order to address thegrowing concern for food deserts. Assume the following table reports the summary statistics for shelf space dedicated to fresh fruits and vegetables (meters) obtained from SRSs of a variety of different stores that supply groceries from each community.
| Community | Average Shelf Space For Fruits and Veg. (m) | Sample Standard Deviation | |
| "Food Desert" | 13.7 | 2.4 | 12 |
| Other Community | 89.4 | 14.6 | 14 |
a) Carry out the appropriate statistical test in order to determine if there is a significant difference in mean shelf space between the two communities at the alpha level of 0.05. Assume all conditions for the test are met. Do not assume equal variances. Write out your null and alternative hypotheses, and correctly interpret your p-value.
b) Construct a 95% confidence interval for your estimate for the average difference in shelfspace provided for fresh fruits and vegetables. Provide an interpretation for your interval.
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