Question

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample variance?

Answer 1

To calculate the sample variance for a set of newborn infant weights, you subtract the mean weight from each weight, square these deviations, sum them, and divide by the number of samples minus one. In this case, the sample variance is
`1.3169 pounds^2`.

Step-by-step explanation:

The question asks to calculate the sample variance for the weights of newborn infants given a sample. To do this, one would follow these steps:

1. First, calculate the mean (average) of the sample weights.
2. Next, subtract the mean from each of the individual sample weights to find the deviations.
3. Square each of the deviations.
4. Add up all the squared deviations.
5. Finally, divide the sum of the squared deviations by the sample size minus one (n-1) to find the sample variance.

For the given data (9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds):

1. The mean weight = (9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6) / 7 = 52.9 / 7 = 7.557 pounds.
2. Subtract this mean from each of the weights and square the result (e.g.,
   `(9.0-7.557)^2`,
   `(7.3-7.557)^2`, etc.).
3. Sum the squared deviations:
4. 3.0995 + 0.06589 + 2.4256 + 1.5432 + 0.05861 + 0.7084 + 0.00014 = 7.9013.
5. The sample variance is 7.9013 / (7-1) =
   `1.3169 pounds^2`.