EXERCISES 353 A nutritionist wants to study the effect of age on muscle mass (in

Question

EXERCISES 353 A nutritionist wants to study the effect of age on muscle mass (in 5.52 120 milligrams per ml) for women. 100 graph displays the boxplots for s divided by age into four groups: E Suppose that the following the muscle-mass measurements for the population of all women, 60 40 (a) What is the response variable? 20- (b) What is the explanatory variable? 0 [40 to 49 years] [S0 to 59 years) (60 to 69 year) 10 to 79 yeans (c) Based on the graph, would the best design for sampling from this population be sim- Age Group ple random sampling, stratified random sampling, or cluster sampling? Explain your answer. (d) Based on the graph, what percentage of women in the oldest age group have a muscle (e) Complete this sentence: Based on the graph, 25% of the women in the youngest age (f) The distribution of muscle mass for women in the 60s age group is symmetric. (8) The 50s age group had a woman with the lowest muscle mass among all women. (h) The IQR for the youngest age group is 50 mass of 80 or less? group have a muscle mass of at least Select one: true false Select one: can't tell can't tell %. true false Select one: true false can't tell What does the plot suggest about the relationship of muscle mass and age? (1) There is no relationship between the two variables (i) A woman's muscle mass decreases with age. (ii) The relationship is skewed to the right.

Explanation / Answer

(a) Muscle mass is the response variable as it is the dependant variable or the outcome variable which depends upon the age of women

(b) Age of women is the explanatory variable as it is used to explain variability in the response variable, also known as an independent variable or predictor variable

(c) Startified random sampling as it works best when a heterogeneous population is split into fairly homogeneous groups (like age) like in this example age is divided into 4 groups. Under these conditions, stratification generally produces more precise estimates of the population percents than estimates that would be found from a simple random sample.

(d) 70 to 79 years is the oldest age group and Q3 = 80 so 75% of women will lie below the third quartile

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