Answer Short Review Questions For Test 3 1. (a) State the Central Limit Theorem. (b) Let x be a random variable from any population with mean and standard deviation . What type of distribution will the distribution for x from samples of size n with n large approximate? 2. Find the mean and standard deviation for the distribution for x based on a random sample of size 64 from a population with mean 37 and standard deviation 24. 3. Find the mean and standard deviation for the distribution for x based on a random sample of size n from a population with mean and standard deviation . 4. What conditions on a sample are necessary in order to find a confidence interval for a proportion? 5. What conditions are necessary in order to find a confidence interval for a mean with a large sample? 6. If a population has a standard deviation of 5, what sample size would be necessary in order for a 99% confidence interval to estimate the population mean within 2? 7. What size of random sample is needed by the Gallup organization to estimate a population proportion within .02 with 90% confidence? In your calculation assume that there is no preliminary estimate for p. 8. Repeat #7, but assume that there is a preliminary estimate that p = .33. 9. Suppose you are to construct a 95% confidence interval for the mean using a sample of size n = 19 from a normal population with unknown standard deviation. What value of tc would s you use in the formula x tc ? n 10. Suppose you are to construct a 92% confidence interval for the mean using a large sample, what value of zc would you use? 11. Which method (large sample/small sample) would you use to find a confidence interval from a normal population with known standard deviation given a sample size of 15? 12. What formula do you use for finding confidence intervals for: (i) means using large samples; (ii) means using small samples; (iii) proportions; (iv) difference of two means; (v) difference of two proportions? 13. Find the critical region for a two-tailed hypothesis test on a mean that is conducted using a large sample at a level of significance = of .01. 14. Find the critical region for a right-tailed test on a proportion at a level of significance = .04. 15. Find the critical region for a left-tailed test on a large sample mean at a level of significance = .04. 1
16. If you reject the null hypothesis when it is true, what type of error have you committed? 17. If you fail to reject the null hypothesis when it is false, what type of error have you committed? 18. Suppose you found a z-value of -8.05 in a right-tailed hypothesis test at a level of significance of = .05, would you reject the null hypothesis? 19. Suppose you found a z-value of -8.05 in a two-tailed hypothesis test at a level of significance of = .05, would you reject the null hypothesis? 20. What do you call the maximum probability at which you are willing to risk making a type I error? 21. Suppose you are conducting a two-tailed test on the mean and arrive at a sample statistic of z = 1.4, what Pvalue would you report? 22. Suppose you are conducting a two-tailed test on the mean and arrive at a sample statistic of z = -1.72, what Pvalue would you report? 23. If you find a Pvalue of .03 for an hypothesis test, what is the probability that the alternative hypothesis is true? 24. Suppose you conducted a left-tailed t...