Question

A study of iron deficiency among infants compared blood hemoglobin levels of a random sample of infants who had been breast-fed to a random sample of infants who had been fed with standard infant formula. Here are the results. Breast-fed infants: n=23 x=13.3 s=1.7 Formula-fed infants n=19 x=12.4 s=1.8 We want to test H0 : µB −µF = 0 , Ha : µB −µF ≠ 0 , where µB and µF are the population mean blood hemoglobin levels for breast-fed and formula-fed infants, respectively. (a) What additional information would you need to confirm that the conditions for this test have been met? (b) Assume the conditions have been met. Calculate the standardized test statistic and P-value for this test. (c) What conclusion would you make at the α = 0.05 significance level? (d) Given your conclusion in part (c), which type of error, Type I or Type II, could you have made? Describe that error in the context of this study

Answer 1

Let the Breast-fed infants be 1 and formula-fed infants be 2. Then,

A.

Populations are normally distributed

Samples were independent and randomly selected

Homogeneity of variance among both populations

B.

df = n1 + n2 - 2

= 40

p-value = 0.1041

C.

Since p-value = 0.1041 > 0.05 i.e. we fail to reject H0 and hence we can't say that blood haemoglobin levels (i.e. iron deficiency) of the two groups differ.

D.

Type 2 error:

Fail to reject H0 when it is false.

The impact of this error is that we will end up concluding that there is no difference in the occurrence of iron deficiency in the two group while there actually is.

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