Sleeping Time I want to analyze the sleeping time of friends and family. I expect my range to lie between 7-8 hours. I want to test the hypothesis if average number of hours of sleep is greater than 8. I ask my face-book friends about the average number of hours they sleep in a week. I also note their gender. The age group I select is 18 - 25. The data is given below. Xi 10 7 4 7 8 10 7 4 8 7 7 8 7 9 6 10 10 6 9 5 10 8 4 9 9 6 6 5 9 4 # OF HOURS OF SLEEP Dates Data Collected 1/30 1/30 2/1 1/30 1/31 2/3 1/31 2/2 2/1 2/3 2/3 2/1 2/4 2/1 2/1 2/4 2/2 2/1 2/4 2/2 2/3 2/2 2/3 2/4 2/4 2/2 2/1 2/2 2/2 2/3 Z Scores 1.360 -0.151 -1.662 -0.151 0.353 1.360 -0.151 -1.662 0.353 -0.151 -0.151 0.353 -0.151 0.856 -0.655 1.360 1.360 -0.655 0.856 -1.159 1.360 0.353 -1.662 0.856 0.856 -0.655 -0.655 -1.159 0.856 -1.662 4 4 5 6 7 8 9 10 Grand Total 2 4 6 4 5 5 30 Hours HISTOGRAM 7 6 5 4 % of HOURS OF SLEEP 3 2 1 0 4 5 6 7 HOURS OF SLEEP 8 9 10 Total of Hours Slept 7 6 5 4 Total 3 2 1 0 4 5 6 7 8 9 10 The various descriptive statistics is given below. 5. Sample variance 7.3 hours of sleep 7 7 6 3.941379 hours of sleep 6. Sample standard deviations 1.985291 hours of sleep 1. Sample mean 2. Sample median 3. Sample mode(s) 4. Sample range 7. Coefficient of variations 27.20% The average number of hours of sleep is 7.3 hours Sample median is 7. This implies half of my friends sleep less than 7 hours and other half sleep more than 7 hours. Mode is the number which has the maximum frequency, here mode is 7. Range is the difference between maximum and the minimum value here range is 6. Sample variance and standard deviation are the measures of dispersion. Variance is measures in squared units and standard deviation is measures in true units. The low values of variance and standard deviation implies mean is reliable. The coefficient of variation is a measure of spread that describes the amount of variability relative to the mean. Here coefficient of variation is 27.20%. Z score indicates how many standard deviations an element is from the mean. Z score is given by (X-mean)/sd. Z-score greater than 3 and less than -3 are considered as outlier. The z scores are given below. The histogram and percentage polygon showed a negative skew. Sine the mean hours of sleep were greater than the median which indicated a positive skewed there were no outliers since there was not a Z score greater or less than -3