Question

A researcher claims that the mean cost of raising a child from birth to age 2 by husband­wife families in the U.S. is $13,960. A random sample of 500 children (age 2) has a mean cost of $13,725. Assume the population standard deviation is $2345. At α = 0.10, is there enough evidence to reject the claim?

Answer 1

Answer:

Yes, there enough evidence to reject the claim.

Step-by-step explanation:

Here we need to perform a test for single mean to determine whether the  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is $13,960.

The hypothesis is:

H₀: The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is $13,960, i.e. µ = $13,960.

Hₐ: The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is different from $13,960, i.e. µ ≠ $13,960.

The information provided is:

$\ar x=13725\\\sigma=2345\\n=500\\\alpha =0.10$

The test statistic is:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{13725-13960}{2345/\sqrt{500}}=-2.24$

The test statistic value is -2.24.

Compute the p-value for this test statistic value at 10% level of significance as follows:

$p-value=2\times P(Z$

               $=2\times 0.01255\\=0.0251$

Use the z-table.

The calculated p-value is, 0.0251 < 0.10, therefore the null hypothesis will be rejected.

Conclusion:

As the null hypothesis is rejected at 10% level of significance it can be concluded that there enough evidence to reject the claim.

The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is different from $13,960.