Answer to Question #329783 in Statistics and Probability for Paula

Question

A sociologist believes that it costs more than P90,000 with a standard deviation of

P4,500 to raise a child from birth to age one. A random sample of 49 families, each with

a child is selected to see if this figure is correct. The average expenses for these families

reveal a mean of P92,000. Based on these sample data, can it be concluded that the

sociologist is correct in his claim? Use 0.05 level of significance.

Step:

1.State the null and alternative hypothesis

concerning the population mean, $\mu$ and the

type of test to be used

2. Specify the level of significance $\alpha$

3. State the decision rule.

4. Collect the data and perform calculations.

5. Make a statistical decision.

6. State the conclusion.

Answer 1

$1:\\H_0:\mu \leqslant 90000\\H_1:\mu >90000\\Z-test\\2:\\\alpha =0.05\\3:\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}>z_{1-\alpha}=z_{0.95}=1.6449\\4:\\Z=\sqrt{49}\frac{92000-90000}{4500}=3.11111\\5:\\3.11111>1.6449\Rightarrow H_0\,\,is\,\,rejected\\6: \\The\,\,claim\,\,that\,\,the\,\,\cos t\,\,is\,\,more\,\,than\,\,90000 is\,\,supported.$