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 Set
Solutions
Name: Lowenbrau Date: 5/9/2015
Problem Number Solution
1. (a) FALSE
(b) FALSE
(c) FALSE
(d) TRUE
(e) FALSE
Work:
(a) If all the observations in a data set are identical, then its variance is equals to zero.
(b) Since A and B are disjoint, the probability of their intersection must be equal to zero,
not equal to 0.9.
(c) For a symmetric distribution if 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 this right 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..
Solutions
Name: Lowenbrau Date: 5/9/2015
Problem Number Solution
1. (a) FALSE
(b) FALSE
(c) FALSE
(d) TRUE
(e) FALSE
Work:
(a) If all the observations in a data set are identical, then its variance is equals to zero.
(b) Since A and B are disjoint, the probability of their intersection must be equal to zero,
not equal to 0.9.
(c) For a symmetric distribution if 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 this right 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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Subject
Statistics