Final answer:
To test the claim that the standard deviation of birth weights of Chinese babies is equal to 567 g, the chi-square test for variability is used. The null hypothesis states that the population variance equals 567 squared grams squared, and it is tested against an alternative hypothesis with a significance level of 0.01.
Step-by-step explanation:
To test the claim that the standard deviation of birth weights of Chinese babies is equal to 567 g, we use the chi-square test for variability. With a sample of 81 Chinese babies with a mean birth weight of 3245 g and a standard deviation of 466 g, we want to test if there is a significant difference compared to the standard deviation of 567 g for Caucasian babies.
We will formulate the hypotheses as follows:
- H0: σ^2 = 567^2 (The population variance is 567 squared grams squared.)
- Ha: σ^2 ≠ 567^2 (The population variance is not 567 squared grams squared.)
The test statistic for this hypothesis test is calculated using the formula:
Chi-square statistic = (n - 1)s^2 / σ^2
where n = 81 (the sample size), s = 466 g (the sample standard deviation), and σ = 567 g (the claimed population standard deviation).
Plugging in the values, we get:
Chi-square statistic = (81 - 1) * 466^2 / 567^2
The calculated chi-square statistic is then compared against the chi-square distribution table value with n - 1 degrees of freedom (80 in this case), at the chosen significance level of 0.01 to determine if the null hypothesis can be rejected.