A nonprofit organization is asking for donations. It hopes to design an email campaign that will ensure it receives at least $50,000. The campaign will reach 10,000 donors and receive donations with a mean of $10 and a standard deviation of $5. Which measure should be used to determine the probability of the campaign receiving $50,000?
Z-score should be used to determine the probability of the campaign receiving $50,000.
The Z-score allows us to assess how many standard deviations a specific value (in this case, $50,000) is from the mean of the donations. By using the Z-score, we can calculate the probability of achieving or exceeding this target based on the given mean and standard deviation of donations.
The median represents the middle value in a data set and does not provide information about the distribution of donations or the probability of reaching a specific target like $50,000. While it can indicate the central tendency of the donations, it does not account for the variability or spread of the data necessary for probability calculations.
The Z-score is the most appropriate measure for this situation as it quantifies how far $50,000 is from the mean donation of $10,000 (10,000 donors * $10 mean donation). By calculating the Z-score, we can determine the likelihood of reaching the $50,000 goal based on the distribution of donations, making it a crucial statistical tool for this analysis.
R-squared measures the proportion of variance in the dependent variable that can be explained by the independent variable(s) in regression analysis. It is not relevant for calculating probabilities related to a specific donation target, as it does not provide a direct measure of how likely the campaign is to reach $50,000.
The T-statistic is used in hypothesis testing to determine if there is a significant difference between means when sample sizes are small or when the population standard deviation is unknown. In this scenario, it does not assist in calculating the probability of reaching a specific donation amount, making it inappropriate for this context.
To assess the probability of the campaign receiving at least $50,000 from donations, the Z-score is the ideal measure. It effectively utilizes the mean and standard deviation of donations to provide a statistical assessment of how likely it is to meet or exceed the donation goal. The other options, while useful in different contexts, do not address the specific needs of this probability calculation.
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