Question

5) Among a sample of 75 students selected at random from one college, the mean number of siblings is 1.4 with a standard deviation of 1.2. Find a 95% confidence interval for the mean number of siblings for all students at this college.

Answer 1

Remember that on a normal distribution, 95% of the cases fall between an interval of radius 2 times the standard deviation around the mean. This is, 95% of the cases are inside the interval:

`\lbrack\bar{x}-2\sigma,\bar{x}+2\sigma\rbrack`

If the mean is equal to 1.4 and the standard deviation is 1.2, then:

`\begin{gathered} \bar{x}-2\sigma=1.4-2(1.2) \\ =-1 \end{gathered}`
`\begin{gathered} \bar{x}+2\sigma=1.4+2(1.2) \\ =3.8 \end{gathered}`

Observe that it is not possible for a student to have less than 0 siblings. Then, the cases in the interval [-1,0) are not real-life cases.

Mathematically, the answer would be:

`\lbrack-1,3.8\rbrack`

Which is the interval of 95% confidence for a normal distribution with mean 1.4 and standard deviation of 1.2