Question

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 7.1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 6.1, 8.1, 9.1, 10.1, 7.1, 11.1, and 12.1 pounds. What is the sample variance?

Answer 1

The sample variance is 4.39 pounds squared.

Step-by-step explanation:

The sample variance is a measure of the spread or dispersion of data within a sample. To calculate the sample variance, we first need to find the mean of the sample, which is calculated by summing up all the weights and dividing by the number of infants in the sample.

Using the weights provided, we can calculate the mean as follows:

Mean = (6.1 + 8.1 + 9.1 + 10.1 + 7.1 + 11.1 + 12.1) / 7 = 8.4 pounds

Next, we calculate the squared differences between each weight and the mean:

(6.1 - 8.4)^2 = 5.76
(8.1 - 8.4)^2 = 0.09
(9.1 - 8.4)^2 = 0.49
(10.1 - 8.4)^2 = 2.89
(7.1 - 8.4)^2 = 1.69
(11.1 - 8.4)^2 = 7.29
(12.1 - 8.4)^2 = 13.69

Finally, we calculate the average of the squared differences, which gives us the sample variance:

Sample variance = (5.76 + 0.09 + 0.49 + 2.89 + 1.69 + 7.29 + 13.69) / 7 = 4.39 pounds squared.