Question

 The average family size in the Philippines was reported as 4.25. A random of families in a particular street resulted in the following family sizes: 5, 6, 7, 4, 3, 2, and 9. At 𝛼=0.10, does the average family size more than the national average?

Answer 1

Assume that the population is normally distributed.

$H_0:\mu=4.25$

$H_1:\mu>4 .25$

$\bar X =5.143$

$s=2.41$

$n=7$

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$

$t=\frac{5.143-4.25}{\frac{2.41}{\sqrt{7}}}$

$=0.98$

$Cv=t_{0.1,6}=1.44$

Since the test statistic 0.98<1.44, we fail to reject the null hypothesis. The is no sufficient evidence to support the claim that the average family size is more than the national average of 4.25.