Answer in Statistics and Probability for Carrie #251397
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]
“H_0: mu = 2 \nnH_1: mu < 2 \nnn=15 \nnbar{x} = frac{2+3+…+3+1}{15} = 1.4 \nns = 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}} \nnt = frac{1.4-2}{1.06 / sqrt{15}} = -2.19 \nnu03b1=0.1 \nndf = n-1 = 14”
Critical value
“t_{14,0.10}= -1.35”
Reject H0 if “|t|> |t_{n-1,u03b1}|”
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.
