# A researcher was interested in the effectiveness of a new drug for testosterone replacement in adult men between the ages of 40 and 59 in the U.S. who

A researcher was interested in the effectiveness of a new drug for testosterone replacement in adult men between the ages of 40 and 59 in the U.S. who are experiencing symptoms related to abnormally low testosterone levels. According to the 2010 Census data, there were 36,135,061 men between the ages of 40 and 59 in the U.S. 100 U.S. men participated in a clinical trial of the drug. Those 100 men were classified by race and ethnicity (White, Asian, Black, Hispanic, Native, Islander, Other) and their average testosterone level was 275 $\frac{ng}{dL}$. The average testosterone level of all adult men in the U.S. between 40 and 59 is 565 ng/dL. Use this information for problems A-E
A. Describe the population.
B.. What is the sample?
C, Identify the parameter(s) and give their value(s).
D. Identify the statistic(s) and give their value(s).
E. Which of the variable(s) are categorical and which are numerical?
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(a) The population contains all $\frac{\text{individuals}}{\text{subjects}}$ about which we want to collect information.
Population = All adult men in the U.S. between the ages of 40 and 59 that are experiencing symptoms related to abnormally low testosterone levels.
(b) A sample is the part of the population of which information was actually collected.
Sample = 100 adult men in the U.S. between the ages of 40 and 59 that are experiencing symptoms related to abnormally low testosterone levels and that participated in the clinical trial of the drug.
(c) A parameter is a descriptive measure for a population.
We know that there are 36,135,061 men in the U.S. between the ages of 40 and 59, but these are not the men with low testosterone levels and thus this gives no information about the population.
We also know that the average testosterone level in all adult men in the U.S. is 565 ng\dl. The average in a population represents the population mean $\mu \mu =565\frac{ng}{dl}$
(d) A statistic is a descriptive measure for a sample.
The average testosterone level of the men in the sample is 275 ng\dl. The average in a sample represents the sample mean $\stackrel{―}{x}.$

(e) The variables are the topics that were investigated.
Variables = Ethnicity, testosterone level.
Categorical/qualitative variables places the individuals into a category, while a quantitative variable is a numerical variable.
Ethnicity = Categorical, as the possible categories are white, Asian, Black, Hispanic, etc.
Testosterone level = Numerical, because the values of the average testosterone levels are numerical.