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

Yes, there enough evidence to reject the claim.

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=(\bar x-\mu)/(\sigma/√(n))=(13725-13960)/(2345/√(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* P(Z<-2.24)`

`=2* 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.