A study of iron deficiency among infants compared samples of infants following d
ID: 3176496 • Letter: A
Question
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 n x s
Breast-fed 22 13.3 1.6
Formula 20 12.5 1.7
a. Carry out a t test. Give the P-value. (Use = 0.01. Use breast-fed formula. Round your value for t to three decimal places, and round your P-value to four decimal places.)
b. Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. (Round your answers to three decimal places.)
(_____,_____)
t = P-value =Explanation / Answer
a) Null Hypothesis = Ho = µ(breast) - µ(formula) = 0
Alternative hypothesis = Ha = µ(breast) - µ(formula) > 0
t statistic = (13.3 - 12.5) / (1.62/22 + 1.72/20)0.5 = 1.56633 = 1.566
p value - degrees of freedom = 22+20-2 = 40. With the t table we see that it is between 0.10 and 0.05. p value = 0.0626
At alpha=0.01, we can not reject the null hypothesis.
b) To calculate the confidence interval, first we can calculate Standard error as below:
SE = sqrt [ s1^2 / n1 + s2^2 / n2 ] = (1.62/22 + 1.72/20)0.5 = 0.5107481
Margin of error = Critical value x Standard error of the statistic
Margin of error = 1.96 * 0.5107481 = 1.001066
Confidence interval = (13.3 - 12.5) +- Margin of error
= 0.8 +- 1.001066
= -0.201066 to 1.801066
So confidence interval is between -0.201 to 1.801
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