First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor. (Ch9) Question 1.1. (Points : 8) True False A response bias (measurement error) may occur more in Census than in Sample. (Ch9) (Points : 8) Question 2.2. True False When the null hypothesis is not rejected, there is no possibility of making a Type I error. (Ch10) (Points : 8) Question 3.3. True False Question 4.4. If n=20 and p=.4, then the mean of the binomial distribution is 8 (Ch6) (Points : 8) True False The level of significance indicates the probability of rejecting a false null hypothesis. (Ch10) Question 5.5. (Points : 8) True False Question 6.6. As the level of significance increases, we are more likely to reject the null hypothesis. (Ch10) (Points : 8) True False A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter. (Ch8) Question 7.7. (Points : 8) True False If p=.8 and n=50, then we can conclude that the sampling distribution of the proportions is approximately a normal distribution. (Ch8) (Points : 8) Question 8.8. True False For a binomial probability experiment, with n=150 and p=.2, it is appropriate to use the normal approximation to the binomial distribution. (Ch7) Question 9.9. (Points : 8) True False If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1p) is larger than when it is smaller. (Ch9) Question 10.10. (Points : 8) True False A continuous random variable may assume only integer values in a given interval. (Ch7) Question 11.11. (Points : 8) True False Everything else being constant, increasing the sample size decreases the probability of committing a Type II error. (Ch10) Question 12.12. (Points : 8) True False If events A and B are mutually exclusive, then P(A and B) is always equal to zero. (Ch5) Question 13.13. (Points : 8) True False If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean. (Ch7) Question 14.14. (Points : 8) True False Question 15.15. A Type II error is failing to reject a false null hypothesis. (Ch10) (Points : 8) True False Question 16.16. A standard normal distribution has a mean of _____ and standard deviation of _____. (Ch7) (Points : 12) Zero, Zero Zero, One One, One One, Zero The set of all possible experimental outcomes is called a(n): (Ch5) (Points : 12) Question 17.17. Sample space Event Experiment Probability None of the above When determining the sample size, if the value found is not an integer initially, the next highest integer value will ____________ be chosen. (Ch9) (Points : 12) Always Question 18.18. Sometimes Never Which of the following signs would not be used in stating a null hypothesis? (Ch10) Question 19.19. (Points : 12) = < 1 and 2 Of all individual tax returns, 37% include errors made by the taxpayer. If IRS examiners are assigned randomly selected returns in batches of 12, find the mean and standard deviation for the number of erroneous returns per batch. (Ch6) Question 20.20. (Points : 12) =2.80, standard deviation =1.67 =4.44, standard deviation =1.67 =4.44, standard deviation =2.80 =7.56, standard deviation =2.80 The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: More than 33.2? (Ch7) Question 21.21. (Points : 12) 43.32% 6.68% 93.32% 86.64% 13.36% Question 22.22. The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. A rule of thumb for ensuring that n is sufficiently large is: (Ch8) (Points : 12) np 10 n(1-p)>= 10 np(1-p) 10 n(1-p) 10 and np 10 np 10 and n(1-p) 10 All of the following are assumptions of the error terms in the simple linear regression model except (Ch13) Question 23.23. (Points : 12) Errors are normally distributed Error terms are dependent on each other Error terms have a mean of zero Error terms have a constant variance Error terms are independent of the Explanatory variable Question 24.24. (Points : 12) H0 is rejected H0 is not rejected H0 may or may not be rejected depending on the sample size n Additional information is needed and no conclusion can be reached about whether H0 should be rejected A six faced fair die is rolled 36 times. Let X be defined as the number of times an even number appears. What is the standard deviation of the variable X? (Ch6) Question 25.25. (Points : 12) 18 9 6 3 1.732 The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both event X and Y (Ch5) (Points : 12) . Complement Question 26.26. Union Intersection Multiplicative probability The width of a confidence interval will be: (Ch9) (Points : 12) Narrower for 99% confidence than for 90% confidence Question 27.27. Wider for a sample size of 64 than for a sample size of 36 Wider for a 99% confidence than for 95% confidence Narrower for sample size of 25 than for a sample size of 36 None of the above Question 28.28. The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario? (Ch10) (Points : 12) H0: =7.5 and HA: 7.5 H0: 7.5 and HA: > 7.5 H0: 7.5 and HA: < 7.5 H0: <7.5 and HA: 7.5 H0: > 7.5 and HA: 7.5 In the most recent election, 19% of all eligible college students voted. If a random sample of 20 students were surveyed, find the probability that exactly half (that is 10 out of 20) voted in the election. (Ch6) Question 29.29. (Points : 12) 0.0000 0.0014 0.0148 0.4997 A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. If all answers were guesses, find the probability of getting exactly four correct answers. (Ch6) Question 30.30. (Points : 12) 0.0604 0.1325 0.2552 0.8000 The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls are selected. What percentage of sample means will be less than 5.15 inches? (Ch8) Question 31.31. (Points : 25) A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .05, test whether the completion time has increased. Question 32.32. (form the hypotheses, show the critical and calculated values of the test statistic and perform the test) (Ch10) (Points : 25) Question 33.33. Based on a random sample of 25 units of product X, the average weight is 104 lbs. and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. What is the critical value (given in terms of the value of the test statistic) at=.01? What is the calculated value of the test statistic? form the hypotheses according to the question and perform the test at 1% significance level. (Ch10) (Points : 25) Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes. (Ch7) Question 34.34. (Points : 25) The probability that an appliance is in repair is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial. Question 35.35. (Ch7) (Points : 25) The College Student Journal (December 1992) investigated differences in traditional and nontraditional students, where nontraditional students are defined as 25 years or older and working. Based on the study results, we can assume the population mean and standard deviation for the GPA of nontraditional students is =3.5 and =0.5. Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated. What is the probability that the random sample of 100 nontraditional students have a mean GPA greater than 3.65? (Ch8) Question 36.36. (Points : 25) The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 100 calculators are selected at random, what is the standard deviation of the number of defectives? (Ch6) Question 37.37. (Points : 25) A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising Question 38.38. expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. X =24 X2=124 Y = 42 Y2 =338 XY =196 Calculate the coefficient of determination and the coefficient of correlation between X and Y Interpret the coefficient of Determination. also find the . slope and intercept and write the estimated Regression equation. What would the predicted sales of tires be if he spends five thousand dollars in advertising? (Ch13) (Points : 25)