Question

8. The US Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $10,460 with a standard deviation of $1,540. You believe the value of the mean cost is incorrect. So you want to test the claim by selecting a random sample of 900 children (age 2) and find that the mean cost is $10,345. At the 5% level of significance, is there enough evidence to conclude that the mean cost is different from $10,460?

Answer 1

8

Null and alternative hypotheses:

$H_0: \mu = 10,460$

$H_a: \mu \neq 10,460$

Since population standard deviation is given, we will use z test here.

Test statistic

$z = \frac{10345-10460}{1540/\sqrt{900}} = -\mathbf{2.24}$

p - Value = 2*P(z < -2.24) = 0.0251

Since this is less than 0.05, we reject Ho.

There is enough evidence to reject the claim that the mean cost of raising a child from birth to age 2 in a rural area is $10460.