In an examination for a class of 30 students, the following scores were obtained
ID: 2957270 • Letter: I
Question
In an examination for a class of 30 students, the following scores were obtained: 99, 45, 60, 80, 95, 100, 95, 91, 85, 87, 77, 75, 61, 71, 85, 88, 83, 85, 79, 81, 82, 55, 63, 75, 82, 88, 77, 78, 41, and 70.(a) Perform the chi-square test on the data for normal distribution. Is normal distribution acceptable at a 5% significance level?
(b) Perform the K-S test on the data for lognormal distribution. Is lognormal distribution acceptable at a 5% significance level?
(c) Assume that the scores can be modeled by a lognormal random variable. Estimate its two parameters using the method of maximum likelihood.
Explanation / Answer
30 data points were entered Mean = 77.77 95% confidence interval for actual Mean: 72.34 thru 83.19 Standard Deviation = 14.5 High = 100. Low = 41.0 Third Quartile = 87.2 First Quartile = 70.8 Median = 80.50 Average Absolute Deviation from Median = 10.6 John Tukey defined data points as outliers if they are 1.5*IQR above the third quartile or below the first quartile. Following Tukey, the following data points are outliers: 41.0 45.0 KS is not particularly happy calling this data normally distributed: P= 0.14 where the normal distribution has mean= 76.22 and sdev= 17.58 KS says it's unlikely this data is log normally distributed: P= 0.03 where the log normal distribution has geometric mean= 73.89 and multiplicative sdev= 1.324 Hope this will helps you.
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