Question

2. Step 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 summary results on blood hemoglobin levels at 12 months of age: Group 5 Breast-fed Formula 19 13.3 12.4 1.7 1.8 Is there significant evidence that the mean hemoglobin level is higher among breast-fed bables? State H, and H, and carry out a test for the difference M-42 (Index 1 refers to breast-fed babies, and index 2 refers to formula-fed babies). Give the value of the test statistic (to 3 decimal places) and the software approximation for the degrees of freedom (to one decimal place). Fill in the blank: A) - B) df - eBook Answer 1 Answer 2 Continue

Answer 1

Step 1

The given data is summarized as follows:

	Sample 1	Sample 2
Sample size	n1=23	n2=19
Sample mean	11 =13.3	$\bar{x}_2$=12.4
Sample SD	s1=1.7	s2=1.8

The test statistic is given by

11 - 12 t 2 2 + ni n2

13.3 – 12.4 t=- 1.72 1.82 V 23 + 19 0.9 0.5442228309 1.653734369 -1.654 1,82

The df is obtained as

( + ) df (s?mi) 12 (53/n2) - Wi-1 Pla-1

$\Rightarrow df=\frac{(\frac{1.7^2}{23}+\frac{1.8^2}{19})^2}{\frac{(1.7^2/23)^2}{23-1}+\frac{(1.8^2/19)^2}{19-1}}=\frac{0.08772169776}{0.002333170139}=37.59764293\simeq 37.6$

The test statistic is 1.654 and the df is 37.6

The p-value is obtained as 0.053227

As the p-value is more than 0.03, we reject the null hypothesis at 3% level of significance.

Step 2

Thus it can be concluded that breast fed children have higher levels of blood haemoglobin at 0.03 significance level. The correct option is the first option

Step 3

The 95% confidence interval is given by

$((\bar{x}_1-\bar{x}_2)\pm \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\;t_{0.025,37.6})$

$i.e.\;((13.3-12.4)\pm \sqrt{\frac{1.7^2}{23}+\frac{1.8^2}{19}}*2.025102)$

$i.e.\;(0.9\pm 1.102106743)$

So the correct option is the first option

Step 4

The required assumptions are that the observations must be independent and the parent distribution must be Normal. So the correct option is the first option

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