## Related questions with answers

Nondigestible oligosaccharides are known to stimulate calcium absorption in rats. A double-blind, randomized experiment investigated whether the consumption of oligofructose similarly stimulates calcium absorption in healthy male adolescents 14 to 16 years old. The subjects took a pill for nine days and had their calcium absorption tested on the last day. The experiment was repeated three weeks later. Some subjects received the oligofructose pill in the first round and then a pill containing sucrose (which served as a control). The order was switched for the remaining subjects. Here are the fractional calcium absorption data (in percent of intake) for 11 subjects:

Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|

Control | 78.4 | 76.6 | 57.4 | 51.5 | 49.0 | 46.6 | 44.2 | 42.9 | 37.2 | 34.1 | 24.6 |

Oligofructose | 62.0 | 95.1 | 46.5 | 49.4 | 89.7 | 43.8 | 50.3 | 51.6 | 66.6 | 52.7 | 54.0 |

(a) Examine the data. Is it reasonable to use the t procedures?

(b) Do the data support the hypothesis that oligofructose facilitates calcium absorption? Use significance level a 5%.

Solution

Verified(a) Create a histogram. The width of the bars has to be the same and the height has to be equal to the frequency.

Shape: Roughly symmetric/bell-shaped and thus the distribution is roughly normal. Thus it is appropriate to use the $t$ procedures.

Center: $\overline{x}=10.8364$

Spread: $s=18.1512$

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