As can be seen in the graph of country distribution of the top 100 female tennis players, Russia have the highest proportion, account for 14% of 100 sampled female tennis players. Follow by United States and Czech Republic with 8%. France, Australia and Spain have the same proportion with 5%. The rest of other countries contribute to 49% of distribution. b) Consider the 2010 earning distribution of the top 100 female tennis players. Illustrate with a histogram and describe it with appropriate numerical descriptive statistics.
Does this distribution appear to be normally distributed? Use some descriptive statistical tools and statistical test(s) to answer this question. * These histogram are clearly asymmetrical and the superimposed normal curve is a little bit do not fit to them well, infact the histogram are skewed to the right so the sample is non-normal distribution * The sample mean is far above the median. Other important measures of the normality are the skewness and kurtosis. (In normal distribution the values of skew and kurtosis are close to 0).
However in this sample, both of them are large positive. Moreover, we have z-score of skewness is 12. 59 and z-score of kurtosis is 20. 93 indicates respectively a very significant positive skew and very significant kurtosis. * These histogram are clearly asymmetrical and the superimposed normal curve is a little bit do not fit to them well, infact the histogram are skewed to the right so the sample is non-normal distribution.
Both p-value are approximately . 00, so that at 5% level of significance level the earnings distribution is appeared to be non-normal. The points on the PP Plot are scarttered far more loosely around the diagonal. Namely, they tend to be above the diagonal at the lower end of the distribution and below it in the middle. Hence the sample are unlikely to be normal distributed. c) Draw a random sample of 15 female tennis players without replacement from the 2010 population of the top 100 female tennis players and present it in a table.