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?
A) 1.177
B) 6.6
C) 1.385
D) 7.6

Question

Quizplus · Accepted Answer

The formula for calculating variance for a sample is:

s^2 = Σ(xi - x̄)^2 / (n - 1)

Where:
Σ means "sum of"
xi = individual data points
x̄ = sample mean
n = sample size

We are given:
Sample size (n) = 7
Sample mean (x̄) = 7.5 (the sum of the weights divided by 7)

Plugging in the values, we get:

s^2 = ((9-7.5)^2 + (7.3-7.5)^2 + (6-7.5)^2 + (8.8-7.5)^2 + (6.8-7.5)^2 + (8.4-7.5)^2 + (6.6-7.5)^2) / (7-1)
s^2 = 9.67 / 6
s^2 = 1.615

Therefore, the sample variance is 1.385. Option C is the correct answer.

A Hypothesis Regarding the Weight of Newborn Infants at a Community