# Hypothesis Testing

1. Oct 30, 2014

### xsgx

The problem:

A simple random sample of 1862 births of Chinese babies resulted in a mean birth weight of 3171 g and a standard deviation of 428 g
(based on “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants,” by Wen et al., American Journal of Epidemiology, Vol.172, No 10). Use a 0.01 significance level to test the claim that the mean birth weight of Chinese babies is less than the mean birth weight of 3369 g for Caucasian babies.

The attempted solution:

The null hypothesis is that the mean weight of Caucasian babies is the same as the mean weight for Chinese babies Ho: M = 3369, and the alternative hypothesis is that the mean weight for Chinese babies is less so H1: M<3369. For the first step I calculated the test statistic for the student t distribution because the standard deviation of the population is not known;using these values, sample mean=3171, Population mean = 3369(the mean weight in grams for the population of Caucasian babies because we are comparing the mean weight of the Chinese baby sample to the Caucasian baby population mean weight), the sample standard deviation 428, and the sample size 1862 :which gave me a test statistic score T=-0.0107. I used the traditional method of using critical values. With a significance level of .01 and the hypothesis test being left tailed because the alternative hypothesis has a “less than” sign the critical value I calculated using statdisk was T=-2.33. Because the test statistic -0.0107 is far above that critical value I failed to reject the null hypothesis that M(Mean weight for Chinese babies)= 3369 (Mean weight for Caucasian babies).

Last edited by a moderator: Apr 24, 2017
2. Oct 31, 2014

### Staff: Mentor

Do you have a question?

Last edited by a moderator: Apr 30, 2017
3. Oct 31, 2014

### RUber

Parentheses might help you sort out the arithmetic error in your work. Notice that the variance of the mean should always be less than the variance of a single sample. The difference between Chinese and American babies is almost .5 standard deviations. The score for comparing means will be larger than this....01 is way too low.
Also, the T test is not wrong, but you will find that it should be almost exactly the same as the standard normal for a sample size of 428.

4. Oct 31, 2014

### xsgx

Well the question is sort of self evident isn't it? Does my explanation contain any errors?

5. Oct 31, 2014

### Staff: Mentor

I see your explanation, but I don't see a question, such as "Does my explanation contain any errors?"

6. Oct 31, 2014

### xsgx

The null hypothesis is that the mean weight of Caucasian babies is the same as the mean weight for Chinese babies Ho: M = 3369, and the alternative hypothesis is that the mean weight for Chinese babies is less so H1: M<3369. For the first step I calculated the test statistic for the student t distribution because the standard deviation of the population is not known;using these values, sample mean=3171, Population mean = 3369(the mean weight in grams for the population of Caucasian babies because we are comparing the mean weight of the Chinese baby sample to the Caucasian baby population mean weight), the sample standard deviation 428, and the sample size 1862: which gave me a test statistic score T=-19.96233. I used the traditional method of using critical values. With a significance level of .01 and the hypothesis test being left tailed because the alternative hypothesis has a “less than” sign the critical value I calculated using statdisk was T=-2.33. Because the test statistic -19.96233 is far below that critical value I rejected the null hypothesis that M(Mean weight for Chinese babies)= 3369 (Mean weight for Caucasian babies).

Did I miss anything? Are there are problems in my arithmetic, logic, or anything else?

7. Oct 31, 2014

### xsgx

I will be sure to follow the template and to include the question in my next post.