Section 3-3 5.The trend of thinner beauty pageant winners has generated charges

Question

Section 3-3

5.The trend of thinner beauty pageant winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for beauty pageant winners from two different time periods. Find the coefficient of variation for each of the two sets of data, then compare the variation.

BMI (from the 1920s and 1930s) 20.4 21.8 22.1 22.4 20.2 189 18.9 19.4 18.4 19.1 BMI (from recent winners): 19.5 20.3 19.6 20.1 17.8 17.9 19.1 18.9 17.5 16.9

Explanation / Answer

Ans:

1)

orginal data is:

46,48,51,58,66,66

Option A is correct.

2)sample proportion=109/520=0.2096

Test statistic:

z=(0.2096-0.25)/sqrt(0.25*0.75/520)=-2.13

3)

a)509*0.426=217

b) z value for 99% CI is 2.58

95% CI for p

=0.426+/-2.58*sqrt(0.426*(1-0.426)/509)

=0.426+/-0.057

=(0.369,0.483)

c)z value for 80% CI is 1.282

80% CI for p

=0.426+/-1.282*sqrt(0.426*(1-0.426)/509)

=0.426+/-0.028

=(0.398,0.454)

d)99% interval is wider than 80% interval.As the confidence interval widens,the probability that the confidence interval actually contain the population parameter increases.

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