Answer to Question #251397 in Statistics and Probability for Carrie

Question

A survey of the number of children in families in a small town gave the following results.

2 3 1 3 1 2 0 0 1 2 1 0 1 3 1

Does this data provide sufficient evidence that the average number of children per family is less

than 2, at the 10% significance level? Clearly show how you draw a conclusion when you test this

hypothesis. Show calculations of all statistics used.

[20]

Answer 1

$H_0: \mu = 2 \\ H_1: \mu < 2 \\ n=15 \\ \bar{x} = \frac{2+3+...+3+1}{15} = 1.4 \\ s = \sqrt{\frac{(2-1.4)^2+(3-1.4)^2 +...+(3-1.4)^2+(1-1.4)^2}{15-1}}=1.06$

Test-statistic

$t= \frac{\bar{x}-\mu}{s / \sqrt{n}} \\ t = \frac{1.4-2}{1.06 / \sqrt{15}} = -2.19 \\ α=0.1 \\ df = n-1 = 14$

Critical value

$t_{14,0.10}= -1.35$

Reject H₀ if $|t|> |t_{n-1,α}|$

2.19>1.35

Reject the null hypothesis.

There is sufficient evidence to support that the average number of children per family is less than 2 at a 0.1 level of significance.