5. Six healthy three-year-old female Suffolk sheep were injected with the antibi

Question

5. Six healthy three-year-old female Suffolk sheep were injected with the antibiotic Gentamicin at a dosage of 10 mg/kg body weight. Their blood serum concentrations (g/mLi) of Gentamicin 1.5 hours after injection were as follows: {29 26 30 31 23 28}. For these data, the mean is 27.8 and the standard deviation is 2.9.
i. Construct a 95% confidence interval for the population mean

ii. Define in words the population mean that you estimated above.

iii. Is it typical for the 95% confidence interval constructed in the first part to nearly contain all of the observations?


6.Human beta-endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. A researcher conducted a study to investigate whether a program of regular exercise might affect the resting (unstressed) concentration of HBE in the blood. He measured blood HBE levels, in January and again in May, in ten participants in a physical fitness program. The results were as shown in the table.
HBE Level (pg/mLi)
Participant January May Difference
1                     42    22    20
2                     47    29   18
3                     37    9      28
4                       9    9       0
5                     33   26      7
6                    70    36     34
7                     54    38    16
8                     27    32    -5
9                   41    33      8
10                   18    14       4
Mean               37.8 24.8 13.0
SD                   17.6 10.9 12.4
i. Conduct a 95% confidence interval for the population mean difference in HBE levels between January (unstressed level) and May (HBE level possibly perturbed by exercise). (Hint: You need to use only the values in the right-hand column.)

ii. Interpret the confidence interval from the first part - that is explain what the confidence interval tells you about the HBE levels.

iii. Use the SOCR (http://www.socr.ucla.edu/htmls/ana/ConfidenceInterval_Analysis.htmlConfidence) Interval Analysis applet to compute the interval for the population mean difference between January and May (paste in all 4 columns in the data tab, choose mean unknown variance in teh CI Settings tab, map the 4th column, difference, as the data column in the Mapping tab, and finally click Calculate button). Compare these results to your manual calculations.

Explanation / Answer

(27.8-1.96*2.9, 27.8+1.96*2.9)

{22.116, 33.484}

I am 95% confident the population mean is in the interval {22.116, 33.484}

Well when you use such a small N, yes. It should cover two standard deviations, so yes, a good majority even for large N.

37.8-1.96*17.6, 37.8+1.96*17.6={3.304, 72.296}

24.8-1.96*10.9, 24.8+1.96*10.9={3.436, 46.164}

It tells you nothing. The range just got smaller.

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