Question

1.       A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in another group were fed a standard baby formula without any iron supplements. Here are the summary results on blood hemoglobin levels at 12 months of age.

	Mean	STD	Sample size
Breast-fed	13.3	1.7	23
Formula	12.4	1.8	19

Assume that the population variances of the two groups are the same.

a.       Use the t-test to investigate whether the mean hemoglobin level is different between breast-fed infants and infants who were fed standard baby formula. Use ?=0.05. Approximate the p-value using the t-table.

b.       Use the ANOVA F-test to investigate whether the mean hemoglobin level is different between breast-fed infants and infants who were fed standard baby formula. Use ?=0.05. Approximate the p-value using the F-table.

c.       What is the relationship between the t test statistic and the F-test statistic (Hint: check to see if t² = F)? What about the p-values from the t-test and the F-test?

Please show all work, neatly.

Answer 1

a) Two sample t-test: For equal variance test

df= n1+n2-2= 40

The test statistic:

Pooled variance:

P-value:0.104

b) F test:

Grand mean:

P-value: 0.1041

c) For test statistic: t^2= F

P-values are same for the both.