Question

According to the N.Y. Times Almanac the mean family size in the U.S. is $3.18$. A sample of a college math class resulted in the following family sizes:

$5;4;5;4;4;3;6;4;3;3;5;5;6;3;3;2;7;4;5;2;2;2;3;2$

At $\alpha =0.05$ level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

Short answer

There is sufficient evidence to conclude that the mean family size in the U.S is not $3.18$.

Step-by-step solution

Given information 

The sample of $24$families

$5;4;5;4;4;3;6;4;3;3;5;5;6;3;3;2;7;4;5;2;2;2;3;2$

Explanation

State the hypothesis:

The null hypothesis states that the mean family size in the U.S is $3.18$. In symbols:

$H_0:\mu =3.18$

The alternative hypothesis states that the mean family size in the U.S is not $3.18$. In symbols:

$H_0\mu \ne 3.18$

localid="1650279234332" $p-value=0.0357$

The null hypothesis is rejected as the $p-value<0.05$