10. 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?
Answer: A
Z-score
To determine the probability of the campaign receiving at least $50,000, the Z-score is the appropriate measure to use. The Z-score allows for the calculation of how many standard deviations a particular value is from the mean, which is essential in assessing the likelihood of achieving the target donation amount.
A) Z-score
The Z-score is a statistical measure that indicates how many standard deviations an element is from the mean. In this scenario, calculating the Z-score will enable the organization to understand the probability of reaching or exceeding the $50,000 target from the mean donation amount of $10, given the standard deviation of $5. This is the correct choice as it directly applies to the situation of assessing probability based on a normal distribution.
B) T-statistic
The T-statistic is used primarily when dealing with smaller sample sizes or when the population standard deviation is unknown. In this case, the nonprofit organization has a sufficiently large sample size of 10,000 donors and a known standard deviation. Therefore, the T-statistic is not the appropriate measure for determining the probability of reaching the donation goal.
C) Median
The median is a measure of central tendency that represents the middle value of a dataset. While it can provide information about the typical donation amount, it does not give insight into the probability of reaching the $50,000 target. Thus, the median fails to address the specific question of probability related to the total amount of donations.
D) R-squared
R-squared is a statistical measure that represents the proportion of variance for a dependent variable that's explained by an independent variable or variables in a regression model. It is not relevant to this scenario, as the nonprofit is not analyzing relationships between variables but rather assessing the likelihood of a specific total amount of donations. Therefore, R-squared is not applicable in this context.
Conclusion
The Z-score is the definitive choice for measuring the probability of the campaign receiving at least $50,000, as it effectively quantifies the relationship between the target amount and the statistical distribution of donations. In contrast, the T-statistic, median, and R-squared do not provide the necessary framework for understanding the likelihood of achieving the specified fundraising goal.