Need help. Thank you

Question

1.To compare the effect of hospital prenatal nutritional counseling on newborn birth-weights, we conduct a matched-pair study of women who obtain prenatal care at a certain hospital, matching women who have been given the nutritional counseling with those who have not. Our null hypothesis is that there is no difference in birth-weights. For each d, we subtract the birth-weight of the mother who did not receive counseling from the birth-weight of the matched mother who did receive counseling.

We use a one-tailed test (with the right tail) and level of significance 

Suppose our study involves n = 50 matched pairs of women; and we find that the mean difference d (between birth-weights for mothers who have received such counseling and those who have not) is given by  with standard deviation .

The degrees of freedom is 

The value of the test statistic TS = 

The critical value  =

2.Should we conclude the mean birth-weight of children is higher (at level of significance 0.05) when their mothers receive prenatal nutritional counseling? That is, should we reject the null hypothesis (at level of significance 0.05? Using complete sentences, explain clearly how you reached your conclusion (using the critical number)

A or B

1. A. There is sufficient evidence that the mean birth-weight of children is higher when their mothers receive prenatal nutritional counseling.
2.  B. There is not sufficient evidence that the mean birth-weight of children is higher when their mothers receive prenatal nutritional counseling.

Explain please.

3.Now suppose instead our study involves n = 100 matched pairs of women; and we find that the mean difference d (between birth-weights for mothers who have received such counseling and those who have not) is given by  with standard deviation .

The degrees of freedom is 

The value of the test statistic TS =  .

The critical value  =  

4.Should we conclude (for this second study) the mean birth-weight of children is higher (at level of significance 0.05) when their mothers receive prenatal nutritional counseling? That is, should we reject the null hypothesis (at level of significance 0.05? Using complete sentences, explain clearly how you reached your conclusion (using the critical number)

A or B

1. A. There is sufficient evidence that the mean birthweight of children is higher when their mothers receive prenatal nutritional counseling.
2.  B. There is not sufficient evidence that the mean birthweight of children is higher when their mothers receive prenatal nutritional counseling

Explain please.

Answer 1

The degrees of freedom is n-1 = 49 

The value of the test statistic TS = 33/(636/sqrt(50)) = 0.367

The critical value  = 1.677

answer is b since TS < 1.677

The degrees of freedom is n-1 = 99 

The value of the test statistic TS = 33/(636/sqrt(100)) = 0.518

The critical value  = 1.66

answer is b since TS < 1.66