Answer to Question #213032 in Statistics and Probability for Daniel

Question

A study shows that the cost of raising a child from birth to age one is more than Php 92 000. A

random sample of 36 families reveal a mean of Php 95 000 with a standard deviation of Php 5 000.

Based on these sample data, can it be concluded that the study is correct in its claim? Use 0.01 level

of significance.

Answer 1

$H_0: \mu ≤ 92000 \\ H_1: \mu > 92000 \\ n=36 \\ \bar{x}= 95000 \\ s= 5000 \\ α=0.01$

Critical value at 0.01 significance level with df =35 is 2.43

$t = \frac{95000-92000}{5000 / \sqrt{36}}= 3.60$

Since test statistics t > 2.43, we have sufficient evidence to reject H₀.

We conclude at 0.01 level that we have enough evidence to support the claim.