Final answer:
In Mathematics, especially statistics, population variance and standard deviation are calculated using the mean of the data and the deviations of each data point from the mean, with the standard deviation being the square root of the variance. Hypothesis testing involves comparing p-values to significance levels to reach a conclusion about a null hypothesis.
Step-by-step explanation:
The subject of the question is Mathematics since it involves calculating population variance and population standard deviation, which are statistical measures. To compute the population variance and standard deviation, we need the individual donation amounts pledged by the nurses. However, since these values are not provided, a general explanation will be given.
To calculate population variance, you would:
- Find the mean (average) of all the donations.
- Subtract the mean from each donation amount to find the deviation of each donation.
- Square each deviation.
- Sum all squared deviations.
- Divide the sum by the total number of donations to get the population variance.
To calculate population standard deviation:
- Take the square root of the population variance.
Remember that when dealing with a sample rather than the entire population, you would use the sample standard deviation formula which involves dividing by the number of donations minus one (n - 1) instead of the total number (n). Regarding hypothesis testing, such as the one described for determining the incidence of an infectious disease at a nursing home, hypothesis testing involves calculating a p-value and comparing it to a predetermined significance level (e.g., 0.05) to decide whether to reject the null hypothesis.