Statistics Practice Problems for Various Topics, Exams of Statistics

Download Statistics Practice Problems for Various Topics and more Exams Statistics in PDF only on Docsity! Practice Problems Statistics 301 1. True or False (a) The normal approximation to the binomial is appropriate for n = 200 and p = .03 (b) Based on a random sample of size n = 4, the sampling distribution of X̄ has variance = 8. If the sample size is increased to 16, the variance becomes 4 . 2. Let the weight X of books carried in a backpack have a normal distribution with mean 3.7 pounds and standard deviation 1.2 pounds. (a) Find the probability that X is greater than 5.5 pounds. (b) Standardize X. 3. (a) List the conditions for Bernoulli trials. (b) When p = 1/3, find the probability of the sequence SFS in 3 trials (c) When p = 1/3, find the probability of two successes in 3 trials (d) Let X Be the number of S’s in 3 Bernoulli trials. Find the mean and variance of X. 1 4. The population has probability distribution value Probability x f(x) 0 .3 2 .4 4 .3 A sample of size 2 is taken. That is, X1 and X2 have the same distribution as the population and they are independent. (a) Construct and urn and describe a sampling scheme that would have these probabilities. (b) Determine the rest of the sampling distribution of T = X1 + X2 2 − 2 value Probability t g(t) −2 .09 −1 .24 2 .09 5. The amount of PCB’s was measured in 40 samples of soil that were treated with contaminated sludge. The following summary statistics were obtained. x = 3.56 s = .5 p.p.m (a) Obtain a 95% confidence interval for the population mean, µ, amount of PCB’s in the soil. (b) Does µ lie in your interval obtained in Part(a)? (c) Why are you 95% confident about you interval in Part(a)? 6. A company wants to establish that the mean life of a printer ink cartridge is over 9000 copies. The data will consist of data on 81 cartridges. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c) Give the form of the rejection region. 2