STAT 116 Review 3

STAT 116 Review #3 Ch 6 & 7 1. Find the following critical values a) * df t for a 95% t- interval for the mean, with n =21. b) * df t for a 99% t- interval for the mean, with n =56. 2. Find the p-value for the following hypothesis tests a) H 0 : μ = 10 vs H A : μ > 10 with test stat t 20 = 2.37 b) H 0 : μ = 10 vs H A : μ < 10 with test stat t 20 = -2.37 c) H 0 : μ 1 = μ 2 vs H A : μ 1 ≠ µ 2 with test stat t 20 = 2.37 d) H 0 : Gender and job preferences are independent with test stat 78 . 8 2 3   3. A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2, and the standard deviation was 2.1. a. Find the best point estimate of the population mean. b. Find the 95% confidence interval of the mean number of jobs. c. Find the 99% confidence interval of the mean number of jobs. d. Which of the two confidence intervals obtained in the previous parts is wider, the 95% CI or the 99% CI? Which of the two confidence intervals gives a more accurate estimate? 4. In a study using 8 samples, and in which the population is normally distributed but the variance is unknown, the distribution that should be used to calculate confidence intervals is a (A) standard normal distribution. (B) t distribution with 7 degrees of freedom. (C) t distribution with 8 degrees of freedom. 5. A sample of 41 light bulbs had a mean lifetime of 599 hours. A 95% confidence interval for the population mean was 593.8 < μ < 604.2. Which one of the following statements is the correct interpretation of the results? (a) The probability that the population mean is between 593.8 hours and 604.2 hours is 0.95. (b) 95% of the light bulbs in the sample had lifetimes between 593.8 hours and 604.2 hours (c) We are 95% confident that the mean lifetime of all the bulbs in the population is between 593.8 hours and 604.2 hours. (d) None of these are true. 6. For each conjecture, state the null and alternative hypotheses: (a) The average income of new accountants is less than $51,597. (b) The average cost in Canada to raise a child from birth to one year old is $10,000. 7. Multiple studies have concluded that two-stage exams increase knowledge retention for the students comparing with traditional exams. (a) Is this a one-tailed or two-tailed test? Why? State your H 0 and H 1 hypotheses in words. (b) What is a type I error in this context? (c) What is a type II error in this context? (d) In this context, what is meant by the power of the test? 8. Determine whether each statement is true or false. If the statement is false, explain why or correct it. (a) No error is committed when the null hypothesis is rejected.