SOMEONE PLEASE HELP ME ASAP!!!
1. In recent years, there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5'7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences. These measurements for Ken and Barbie and their reference groups are presented in the table below.
Ken Barbie
Chest Waist Hips | Chest Waist Hips
Doll: 75.0 56.5 72.0 | 82.3 40.7 72.7
Human x-bar: 91.2 80.9 93.7 | 90.3 69.8 97.9
Human S: 4.8 9.8 6.8 | 5.5 4.7 5.4
Suppose that the researchers' scaled-up dolls suddenly found themselves in the human world of actual men and women.
Convert Ken's chest, waist, and hips measurements to z-scores. Which of those measures appears to be the most different from Ken's reference group (human males)? Justify your response with an appropriate statistical argument.
2. In recent years, there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5'7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences. These measurements for Ken and Barbie and their reference groups are presented in the table below.
Ken Barbie
Chest Waist Hips | Chest Waist Hips
Doll: 75.0 56.5 72.0 | 82.3 40.7 72.7
Human x-bar: 91.2 80.9 93.7 | 90.3 69.8 97.9
Human S: 4.8 9.8 6.8 | 5.5 4.7 5.4
Suppose that the researchers' scaled-up dolls suddenly found themselves in the human world of actual men and women.
Convert Barbie's chest, waist, and hips measurements to z-scores. Do these z-scores provide evidence to justify the claim that the Barbie doll is too thin of a representation of adult women? Justify your response with an appropriate statistical argument.
3. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normally distributed with the mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6.
Find the standardized scores for both students.
4. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normally distributed with the mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6.
Assuming that both tests measure the same kind of ability, who has the higher score, and why?
5. A lunch stand in the business district has a mean daily gross income of $420 with a standard deviation of $50. Assume that the daily gross income is normally distributed.
If a randomly selected dat has a gross income of $520, then how many standard deviations away from the mean is that day's gross income?
