Statistical Analysis and Probability Evaluation: Comprehensive Problem Set Solutions

A complete set of solved problems in statistical analysis and probability.

Olivia Smith

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Statistical Analysis and Probability Evaluation: Comprehensive Problem SetSolutionsName:LowenbrauDate:5/9/2015Problem NumberSolution1.(a)FALSE(b)FALSE(c)FALSE(d)TRUE(e)FALSEWork:(a)If all the observations in a data set are identical, then its variance isequals tozero.(b)SinceAandBaredisjoint, the probability of their intersection mustbe equal to zero,not equal to 0.9.(c)For a symmetric distributionif P (X> 2)= 0.3, then P (X≤–2) = 0.3, not P (X≤–3)≤0.3.(d)The critical value for 959% confidence level is larger than that of 90% confidence level.So 95% confidence interval has larger width than 90% confidence interval.(e)Since the p-value for thisright tailed test, P (T > 1.5) = 1–P (X < 1.5) = 1–0.96 = 0.04 <0.05, the decision must be reject the null hypothesis is at 0.05 level of significance..

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