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 standard deviation?

Answer 1

Answer: 1.2

Explanation:

Given sample (x) : 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, 6.6

Sample size : n= 7

`\text{Sample mean}=\overline{x}=(\sum x)/(n)\\\\=(52.9)/(7)=7.55714285714\approx7.6`

Formula for sample standard deviation :-

`\sigma=\frac{\sum(x-\overline{x})^2}{n}`

Now,
`\sum(x-\overline{x})^2=(9-7.6)^2+(7.6-7.6)^2+(6-7.6)^2+(8.8-7.6)^2+(6.8-7.6)^2+(8.4-7.6)^2+(6.6-7.6)^2\\\\\Rightarrow\ \sum(x-\overline{x})^2=8.24`

Now,
`\sigma=(8.24)/(7)=1.177142857\approx1.2`

Hence, the sample standard deviation = 1.2