Statistics 101 problem. Using confidence values and z scores?

[famtrecrew]

1. A study of zinc-deficient mothers was conducted to determine whether zinc supplemnetation during pregnancy results in babies with increased weight at birth. The weights are measured in grams. Use a 0.05 significance level to test the claim that zinc supplementation does increase weight at birth



2. Zinc group: n=294 xbar=3214 s=669

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



3. I tried using z scores to figure this out by using the equation z= xbar-m/sigma/[squareroot of n] however i am not sure if i need some sort of hypothesis testing or how to go about solving this. Since i don't know m I was using the xbar1-xbar2 on the numerator. Any help is appreciated. The answer i got was using Hnot: m<=0 and H1: m>0. Then getting 1.96 and a calculated z score of 3.229. Since 3.229>1.96 I stated that we reject Hnot and which means that m is greater than 0 showing a positive weight gain in the zinc supliment category. I think that this is wrong though.

 

[EnumaElish]

xbar1-xbar2 is right; but since the standard devs. and the sample sizes are different, you need to calculate the pooled standard dev. as follows:

http://en.wikipedia.org/wiki/T_test#Unequal_sample_sizes

 

[Architeuthis Dux]

I would start by clarifying the question and the information provided. The question asks to test the claim that zinc supplementation increases weight at birth, but the data provided only includes the weights of the babies in each group. It does not mention whether the mothers in the zinc group were actually given zinc supplementation during pregnancy. This information is crucial in determining whether the claim can be tested.

Assuming that the mothers in the zinc group were indeed given zinc supplementation, the next step would be to formulate the null and alternative hypotheses. The null hypothesis (H0) would be that there is no difference in the weight at birth between babies born to mothers who received zinc supplementation and those who did not. The alternative hypothesis (Ha) would be that there is a difference, specifically an increase, in the weight at birth for babies born to mothers who received zinc supplementation.

Next, I would use the information provided to calculate the z-score and p-value. The z-score can be calculated using the formula provided in the question, where xbar1 and xbar2 are the mean weights of the zinc and placebo groups respectively, and sigma is the pooled standard deviation of the two groups. The p-value can then be determined using a z-table or a statistical software.

If the p-value is less than 0.05, then we can reject the null hypothesis and conclude that there is a significant difference in the weight at birth between the two groups. However, if the p-value is greater than 0.05, we would fail to reject the null hypothesis and cannot conclude that there is a difference in weight at birth between the two groups.

In conclusion, more information is needed to accurately test the claim that zinc supplementation increases weight at birth. Once all necessary information is provided, the appropriate statistical test can be conducted to determine the significance of the results.