Respuesta :
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:
[tex]\ar x=13725\\\sigma=2345\\n=500\\\alpha =0.10[/tex]
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{13725-13960}{2345/\sqrt{500}}=-2.24[/tex]
The test statistic value is -2.24.
Compute the p-value for this test statistic value at 10% level of significance as follows:
[tex]p-value=2\times P(Z<-2.24)[/tex]
[tex]=2\times 0.01255\\=0.0251[/tex]
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.
