Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. A paper gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P).
Subject | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
L | 1927 | 2547 | 2825 | 1923 | 1628 | 2175 | 2111 | 2621 | 1843 | 2543 |
P | 2127 | 2885 | 2895 | 1945 | 1750 | 2183 | 2164 | 2626 | 2006 | 2628 |
(a) Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of 0.05. [Note: The appropriate normal probability plot shows some curvature but not enough to cast substantial doubt on a normality assumption.] (Use μD = μP − μL.)
H0: μD =
25
Ha: μD > 25
H0: μD = 25
Ha: μD <
25 H0:
μD = 25
Ha: μD ≠ 25
H0: μD = 25
Ha: μD ≤ 25
Calculate the test statistic and determine the P-value.
(Round your test statistic to two decimal places and your
P-value to three decimal places.)
t | = | |
P-value | = |
State the conclusion in the problem context.
Fail to reject H0. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g. Reject H0. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g. Fail to reject H0. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g. Reject H0. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g.
(b) Calculate an upper confidence bound using a 95% confidence
level for the true average difference between TBBMC during
postweaning and during lactation. (Round your answer to two decimal
places.)
g
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