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Mathematical Probability Practice Exam

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MAT 1600 – Final Exam Part 1 1. What is an example of a statistic? A statistic is a measurable characteristic used for estimating the value of a population parameter, such as average weight of students in a certain classroom 2. According to what theorem will the sampling distribution of the sample mean will be normal when a sample of 30 or more is chosen? The Central Limit Theorem 3. When is the finite population correction factor used? Only when our sample size is relatively large (more than 5%) with respect to population size 4. What type of sample is chosen in such a way that all elements of the population are equally likely to be chosen? A Simple Random sample 5. If a confidence interval for the population mean is constructed when the population standard deviation is unknown, what is the margin of error? Since population standard deviation is unknown, we’ll be using the t-test, and the margin of error for the t-test is calculated as: 𝑠 𝑑 π‘›βˆ’1 𝛼 ( ) 2 βˆšπ‘› 6. What is the standard deviation of the t-distribution? 𝜈 πœŽπ‘‘βˆ’π‘‘π‘’π‘ π‘‘ = √ , π‘€β„Žπ‘’π‘Ÿπ‘’ 𝜈 = π‘‘π‘’π‘”π‘Ÿπ‘’π‘’π‘  π‘œπ‘“ π‘“π‘Ÿπ‘’π‘’π‘‘π‘œπ‘š = π‘ π‘Žπ‘šπ‘π‘™π‘’ 𝑠𝑖𝑧𝑒 βˆ’ 1 πœˆβˆ’2 7. What is one property that the t-distribution and standard normal distribution have in common? Both distributions have bell-shaped curves 8. Suppose that a confidence interval is constructed at the 95% level. If the confidence interval is increased to ...
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