Show calculations please 1. In a study of the effects of space travel on metabol

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Show calculations please
1. In a study of the effects of space travel on metabolism, a study of 28 rats was conducted One group of 14 male rats were sent to space. Upon return, the red blood cell mass (in mg) of the rats was determined. A control group of 14 male rats was held under the same conditions (except for the space flight) as the space rats, and their red blood cell mass was also determined when the space rats returned. The project, led by Dr. Paul X. Callahan, resulted in the data below. Determine if there is sufficient evidence that the space flight rats have a lower red blood cell mass from the control animals at the = 0.05 level. Red Blood Cell Mass (mg) In Space 8.59 8.64 7.43 7.21 6.87 7.89 9.79 6.85 7.00 8.80 9.30 8.03 6.39 7.54 Control 8.65 7.62 7.44 8.55 8.70 7.33 8.58 9.88 9.94 7.14 9.14 6.99 8.40 9.66 714 858 8ss a) Is this a designed experiment or an observational study? Justify your answer b) Now perform a traditional hypothesis test of the claim that rats in space have a lower mean red blood cell mass using the 4 C's (context, conditions/graphs, calculations, conclusion). Context Conditions Calculations Conclusion

Explanation / Answer

(a) Above given case is an observational study where rats behavior is studied under certain circumstances.

(b) Null Hypothesis : H0: Mass of Red Blood Cell for rats in space is equals to mass of RBC for rats at earth.

Alternate hypothesis : Ha : Mass of Red Blood celss for rats in space is less than the mass of red blood cells for rats at earth.

Sample mean for mass of RBC for rats in space xspace = 7.88 mg

Sample mean for mass of RBC for rats in control xcontrol = 8.43 mg

Standard deviation for mass of RBC for rats in space sspace= 1.02 mg

Standard deviation for mass of RBC for rats in space scontrol = 1.00 mg

pooled standard deviation sp = sqrt [(s2space  + s2control)/2] = sqrt [(1.022 + 1.002)/2] = 1.01 mg

so

Test statistic

t = (xspace - xcontrol)/ sp * sqrt[1/n1+ 1/n2]

t = (7.88 - 8.43)/ 1.01 * sqrt (1/14 + 1/14)

t = -0.55 / 0.3817

t = -1.44

so for alpha = 0.05 and dF = 26

tcr = 2.048

so here t < tcritical so we shall reject the null hypothesis and can conclude that there is no significant difference in mean mass of RBC for rats in space and at control environment.

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