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STAT 231 (84)
Lecture

Tutorial One .pdf

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School
Department
Statistics
Course
STAT 231
Professor
Semester
Fall

Description
Tutorial 1 1. In a particular class of 39 students the number of hours of sleep before a final exam were (ordered from smallest to largest) : 2.3 2.6 2.8 2.8 3.1 3.4 3.5 3.7 3.9 4.1 4.2 4.4 4.4 4.8 4.9 5.1 5.1 5.3 5.3 5.5 5.6 5.6 5.6 5.8 5.8 5.9 5.9 6.2 6.5 6.6 6.9 7.3 7.6 7.7 8.1 8.6 9.2 9.5 10.1 Let y ie the number of hours of sleep for the ith student i  1,…,39. Then 39 39 2 ∑ y i 215.7 and ∑ yi 1338.37 i1 i1 (a) Find the following for these data: (i) sample mean, median, mode (ii) sample variance, sample standard deviation, range (iii) lower or first quartile, upper or third quartile, interquartile range (IQR) (iv) five number summary. Explain, in terms of summarizing the given data, what each of the values means. (b) Suppose Y  G , Find  P |−  ≤ | and PY −  ≤| . De|ermine he intervals y − s,y  s and ̄ ̄  ̄ − 2s,ȳ 2s fr the given data. How many observations occurred in each interval? Comment on this result in light of the probability statements. (c) A relative frequency histogram of the data is given below along with the values of the sample skewness and kurtosis. Comment on whether you think a Gaussian model is a good fit to the data. Sleep Data 0.35 0.3 skewness = 0.71 kurtosis = 5.24 0.25 Density 0.2 0.15 G(5.53,1.96) p.d.f. 0.1 0.05 0 1 2 3 4 5 6 7 8 9 10 Observation (d) At a later time a missing observations was discoverd. If the missing obervation was y
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