Zinc difecient Mother and birth weight problem

[famtrecrew]

Using a study of zinc deficient mothers a double blind test was conducted using a placebo group and a test group. Using a .05 significance level to test a claim that zinc supplimentation does increase weight at birth. The weights are measured in grams. How can I test to see if the zinc suplimentation effected the outcome of birth weight using the following groups of statistics:

Zinc Supplement Group: n=294 xbar=3214 s=669

Placebo Group: n=286 xbar=3088 s=728

 

[EnumaElish]

http://en.wikipedia.org/wiki/T-test#Unequal_sample_sizes

 

[tacman]

To test the claim that zinc supplementation increases birth weight, we can use a two-sample t-test with a significance level of 0.05. This test will compare the mean birth weights of the two groups and determine if there is a statistically significant difference.

First, we need to calculate the pooled standard deviation, which takes into account the sample sizes and standard deviations of both groups. This can be calculated using the formula:

Sp = √[(s1^2 + s2^2) / (n1 + n2 - 2)]

Where s1 and s2 are the standard deviations of the two groups, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

Sp = √[(669^2 + 728^2) / (294 + 286 - 2)] = 703.99

Next, we calculate the t-statistic, which is given by the formula:

t = (xbar1 - xbar2) / (Sp √[(1/n1) + (1/n2)])

Where xbar1 and xbar2 are the sample means of the two groups, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

t = (3214 - 3088) / (703.99 √[(1/294) + (1/286)]) = 2.54

Finally, we can use a t-distribution table or a statistical software to determine the p-value associated with this t-statistic. The p-value is the probability of obtaining a t-statistic as extreme as the one we calculated, assuming that the null hypothesis (that there is no difference in birth weight between the two groups) is true.

If the p-value is less than the significance level of 0.05, then we can reject the null hypothesis and conclude that there is a statistically significant difference in birth weight between the zinc supplement group and the placebo group. This would indicate that zinc supplementation does have an effect on birth weight.

However, if the p-value is greater than 0.05, then we fail to reject the null hypothesis and cannot conclude that there is a significant difference in birth weight between the two groups. In this case, we would need to conduct further studies with larger sample sizes or different study designs to determine the effect of zinc supplementation on birth weight.