Question

18. A sociologist is interested in the effects of racism on birth weight. He constructs a dataset ing the birth weight of African American children (in pounds experience with racism during their pregnancy. He divides the children into two groups -those contain- and their mothers' self-reported whose mothers at least one experience of racism during their pregnancy. Assuming birth rates to be tributed, test the null hypothesis of no difference in mean birth weight between the two groups. reported experiencing no race-related incidents and those whose mothers reported No Exposure Exposure to Racism 7.2 8.4 7.6 6.9 9.2 8.7 6.9 5.4 6.3 6.8 7.2 6.1 5.9 6.8 7.6 7.3 7.4 7.3

Answer 1

Null hypothesis H0: Mean difference in birth weight between children whose mothers experience race-related incidents and not experienced race-related incidents is zero.
Alternative hypothesis H0: Mean difference in birth weight between children whose mothers experience race-related incidents and not experienced race-related incidents is not zero.

For this analysis, assume the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis as we do not know the population standard deviations of the two groups and whether the population standard deviations of the two groups are equal or not.

Let s₁ is the  standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2,  and SE is the standard error.

Mean of sample 1 (No Exposure) = 7.775

Mean of sample 2 (Exposure to Racism) = 6.68

Standard deviation of sample 1 = 0.8779033

Standard deviation of sample 2 = 0.7284687

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)] = sqrt[(0.8779033²/8) + (0.7284687²/10)] = 0.3865306

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

= (0.8779033²/8 + 0.7284687²/10)² / { [ (0.8779033² / 8)² / (8 - 1) ] + [ (0.7284687² / 10)² / (10 - 1) ] }

= 14 (Rounding to nearest integer)

Test statistic, t = (Difference in means) / SE = (7.775 - 6.68) / 0.3865306 = 2.83

P(t > 2.83, df = 14) = 0.0067

For two-tail test, p-value = 2 * 0.0067 = 0.0134

Since the p-value is less than the significance level of 0.05, we reject null hypothesis H0 and conclude that there is significant evidence that mean difference in birth weight between children whose mothers experience race-related incidents and not experienced race-related incidents is not zero.