Assignment

Body Temperature

Machowiak et al. (1992)¹ provided a critical examination of whether normal body temperature was 37^oC. They recorded the orally-determined body temperatures of 65 male and 65 female subjects. Use their results in Table 1 to answer the questions further below.

Table 1: Summary statistics for the body temperature of a sample of men and women.

     n   mean     sd    min     Q1 median     Q3    max 
130.00  36.81   0.41  35.70  36.60  36.80  37.10  38.20 

1. construct statistical hypotheses (make sure to define μ),
2. write the definition of the p-value specific to this question,
3. compute the p-value assuming that σ=0.45 (Show a drawing and the distrib() code that you used),
4. make a decision about the hypotheses using α=0.05 (show you work), and
5. summarize your findings in terms of body temperatures.

Beetle Size

Researchers examined the size of two different species of beetles. They hypothesized that the thorax length of the Halticus oleracea species would be greater than 190 μm. Use their results for the Halticus oleracea species in Table 2 to answer the questions further below.

Table 2: Summary statistics for the thorax length for two species of beetles.

             species  n   mean    sd min     Q1 median     Q3 max
1 Halticus.carduorum 20 179.55 10.09 158 175.75  180.5 181.75 198
2  Halticus.oleracea 18 194.17 14.03 170 189.75  192.0 200.75 221

1. construct statistical hypotheses (make sure to define μ),
2. write the definition of the p-value specific to this question,
3. compute the p-value assuming that σ=15 (Show a drawing and the distrib() code that you used),
4. make a decision about the hypotheses using α=0.05 (show your work), and
5. summarize your findings in terms of the beetle’s thorax size.

Identifying Type I and II Errors

In each situation below, (i) write what H₀ and H_A mean in words, (ii) describe what a Type I and a Type II error is, and (iii) make an argument for which error is more egregious. [Hint: See the example about the rare plant in the module reading.]

1. The United States Department of Agriculture’s (USDA) limit for salmonella contamination for chicken parts is 15.4%.² Suppose that a meat inspector reports that the chicken produced by a particular company exceeds the USDA limit. A hypothesis test will be performed to determine whether the meat inspector’s claim appears to be true or not.
2. The process of manufacturing a certain drug is quite complex. Small departures from the standard procedure can result in a drug that does not meet specifications and is dangerous to the user. Before being released for use, a sample of a batch of the drug is tested to determine if the mean amount of a particular chemical in the drug meets specifications. A hypothesis test will be performed to determine if the drug met specifications or not.