Suppose we have yo estimate the average number of purchases in a given hour in a given hour at a convenient store. Using this example describe in your own words how you would go about this determining this average through:
A.) Drawing a random sample
B.) A Systematic sample
C.) A convenient sample
I just need to know if someone could show me an example to this . I have the questions answer just not answered well enough for my instructor if there is a method of showing this I would appreciate it.
A.) Drawing a random sample: To determine the average number of purchases in a given hour at a convenience store using a random sample, you would start by identifying the population you want to study, which in this case is all the purchases made in a given hour. Next, you would need to assign every purchase in that hour a unique identifier (e.g., a number). Then, using a random number generator or a table of random numbers, you would select a specific number of purchases to include in your sample. For example, if you want a sample size of 50 purchases, you would randomly select 50 unique numbers from the list of identifiers. Finally, you would collect the data (e.g., the number of purchases) for the selected purchases and calculate the average. This average would then estimate the average number of purchases in a given hour at the convenience store.
B.) Systematic sample: To determine the average number of purchases in a given hour at a convenience store using a systematic sample, you would start by assigning every purchase in that hour a unique identifier. Then, you would determine the sampling interval, which is the ratio of the population size to the desired sample size. For example, if you want a sample size of 50 purchases from a population of 500 purchases, the sampling interval would be 500/50 = 10. Next, you would randomly select a starting point between 1 and the sampling interval. This starting point could be determined using a random number generator or by any other randomization method. Once you have the starting point, you would include every nth purchase in your sample, where n is the sampling interval. For example, if the starting point is 3, you would include the 3rd purchase, then the 13th purchase, then the 23rd purchase, and so on, until you reach the desired sample size. Finally, you would collect the data (e.g., the number of purchases) for the selected purchases and calculate the average, which would estimate the average number of purchases in a given hour at the convenience store.
C.) Convenience sample: To determine the average number of purchases in a given hour at a convenience store using a convenience sample, you would simply select the purchases that are most convenient or readily available. This could involve selecting purchases that are closest to you, that are easiest to access, or that you have easy access to the necessary data for. However, it is important to note that a convenience sample is not representative of the entire population and may introduce bias in the estimate of the average. Therefore, while a convenience sample can provide some information, it may not accurately reflect the average number of purchases in a given hour at the convenience store.
A.) Drawing a random sample:
To determine the average number of purchases in a given hour at a convenience store using a random sample, you would follow these steps:
1. Define the population: Identify the entire population from which you want to draw a sample. In this case, it would be all the hours in a given day at the convenience store.
2. Assign a unique identifier: Assign a unique identifier to each hour in the population. You can use the clock time or any other method to identify the hours.
3. Determine the sample size: Decide on the desired sample size. This is the number of hours from which you will collect data.
4. Randomly select hours: Use a randomization method such as a random number generator to select the specified number of hours. You can do this by generating random numbers within the range of unique identifiers assigned to the hours and selecting the corresponding hours.
5. Record the data: During the selected hours, note down the number of purchases made in each hour. Repeat this process for all the selected hours.
6. Calculate the average: Once you have data from all the selected hours, sum up the number of purchases and divide it by the sample size to find the average number of purchases per hour.
B.) Systematic sample:
To estimate the average number of purchases using a systematic sample, follow these steps:
1. Define the population: Identify the entire population of hours at the convenience store, just like in the random sample.
2. Determine the sample size and interval: Decide on the desired sample size, and calculate the sampling interval by dividing the population size by the desired sample size.
3. Choose a starting point: Select a random starting point within the population. You can use a random number generator to determine this starting point.
4. Select the systematic sample: Starting from the randomly chosen starting point, select every nth hour to include in your sample. The value of n is the sampling interval calculated in the previous step.
5. Record the data: During the selected hours, record the number of purchases made in each hour.
6. Calculate the average: After collecting data from the selected hours, calculate the average number of purchases per hour by summing up the number of purchases and dividing it by the sample size.
C.) Convenient sample:
Determining the average number of purchases using a convenient sample is less rigorous and more subjective. Here's an example:
1. Define the population: Identify the population of hours at the convenience store, similar to the previous methods.
2. Choose convenient hours: Instead of randomly or systematically selecting hours, you simply choose hours that are convenient or easily accessible to you personally. These may include peak hours, slow hours, or any other hours that you think will provide representative data.
3. Record the data: During the chosen hours, record the number of purchases made in each hour.
4. Calculate the average: Once you have data from the convenient sample, calculate the average number of purchases per hour by summing up the number of purchases and dividing it by the sample size.
It's worth noting that while a convenient sample is quick and easy, it may not always provide an accurate representation of the population, as there may be biases or shortcomings in the selection process. A random or systematic sample is generally considered more reliable for estimating averages.