Breast feeding sometimes results in a temporary loss of bone mass as calcium is
ID: 3155868 • Letter: B
Question
Breast feeding sometimes results in a temporary loss of bone mass as calcium is depleted in the mother's body to provide for milk production. An investigation gave the following data on total body bone mineral content (g) for a sample of mothers both during breast feeding (B) and in the postweaning period (P).
Do the data suggest that true average total body bone mineral content during postweaning exceeds that during breast feeding by more than 25 g? State and test the appropriate hypotheses using a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Use P B. Round your test statistic to two decimal places and the P-value to three decimal places.)
Conclusion
reject H0
fail to reject H0
Subject 1 2 3 4 5 6 7 8 9 10 B 2672 2010 2403 2763 2592 2338 2810 2529 2546 2360 P 2690 2134 2475 2778 2720 2448 2831 2575 2697 2409Explanation / Answer
The differences are
18
124
72
15
128
110
21
46
151
49
Formulating the null and alternative hypotheses,
Ho: ud <= 25
Ha: ud > 25
At level of significance = 0.05
As we can see, this is a right tailed test.
Calculating the standard deviation of the differences (third column):
s = 54.3186446
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 17.17706364
Calculating the mean of the differences (third column):
XD = 73.4
As t = [XD - uD]/sD, where uD = the hypothesized difference = 25 , then
t = 2.817710933 [ANSWER]
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As df = n - 1 = 9 [ANSWER]
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Also, using p values, as this is one tailed,
p = 0.010061037 [ANSWER]
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As P < 0.05, WE REJECT THE NULL HYPOTHESIS. [ANSWER]