The trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMIs) for Miss American winners from two different time periods. Consider the listed values to be simple random samples selected from larger populations. Using a .05 significance level, test the claim that recent winners have a lower mean BMI than winners from the 1920s and 1930s. Set up your data file so ‘20s and ‘30s winners = 1; recent winners = 2;. BMI (from the 1920s and 30s): 20.4 21.9 22.1 22.3 20.3 18.8 18.9 19.4 18.4 19.1 BMI (from recent winners): 19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- The trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMIs) for Miss American winners from two different time periods. Consider the listed values to be simple random samples selected from larger populations.
- Using a .05 significance level, test the claim that recent winners have a lower
mean BMI than winners from the 1920s and 1930s. Set up your data file so ‘20s and ‘30s winners = 1; recent winners = 2;.
- Using a .05 significance level, test the claim that recent winners have a lower
BMI (from the 1920s and 30s):
20.4 21.9 22.1 22.3 20.3 18.8 18.9 19.4 18.4 19.1
BMI (from recent winners):
19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8
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