48. 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: D
Using a Z-score is appropriate for determining the probability of the campaign receiving $50,000.
To assess the likelihood of receiving at least $50,000 from donations, a Z-score can be calculated, which will help standardize the amount in relation to the mean and standard deviation of the donations. This statistical measure allows the organization to understand how many standard deviations the target amount is from the mean.
A) Median
The median represents the middle value of a data set and does not provide information about the distribution of donations. While it gives a central tendency, it is not suitable for calculating probabilities or understanding how likely the campaign is to meet its financial goal of $50,000.
B) 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 applicable in this context, as the question does not involve regression analysis or the relationship between variables.
C) T-statistic
The T-statistic is used in hypothesis testing to determine whether there is a significant difference between the means of two groups, particularly when sample sizes are small. In this case, since the mean and standard deviation of donations are known, a Z-score is more appropriate than a T-statistic for determining the probability of reaching the donation goal.
D) Z-score
The Z-score measures how far away a particular value is from the mean in terms of standard deviations. It is the correct choice for this scenario because it allows the organization to calculate the probability of receiving $50,000 by standardizing the amount against the known mean and standard deviation of donations.
Conclusion
The Z-score is the most suitable measure for determining the likelihood of the nonprofit organization achieving its donation goal of $50,000, as it effectively utilizes the mean and standard deviation of the expected donations. In contrast, the other options—median, R-squared, and T-statistic—fail to provide the necessary analysis for probability calculations in this context.