Statistics 101 problem. Using confidence values and z scores?

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The discussion focuses on a statistical analysis of zinc supplementation during pregnancy and its effect on birth weight. The zinc group had a sample size of 294 with a mean weight of 3214 grams and a standard deviation of 669, while the placebo group had 286 participants with a mean weight of 3088 grams and a standard deviation of 728. Using a significance level of 0.05, the calculated z-score was 3.229, which exceeds the critical value of 1.96, leading to the rejection of the null hypothesis (H0: m ≤ 0) in favor of the alternative hypothesis (H1: m > 0), indicating a significant positive effect of zinc supplementation on birth weight. The discussion highlights the necessity of using pooled standard deviation due to unequal sample sizes.

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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.
 
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