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1 Name: Date: 1. A sample of 25 different payroll departments found that the employees worked an average of days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked, µ, of all payroll departments? A) < µ < B) < µ < C) < µ < < µ <. D) In 2000 there were almost 300,000 Canadians with more than 1 million dollars in financial assets! If the average age of one hundred randomly selected millionaires was 54.8 years with a standard deviation of 7.9 years, what is the 95% confidence interval for the mean age, µ, of all Canadian millionaires? A) 53.5 < µ < 56.1 B) 53.3 < µ < 56.3 C) 52.8 < µ < 56.8 D) 51.7 < µ < The average number of miles that 90 truckers drove in a day was 540 with a standard deviation of 40 miles. What is the 99% confidence interval of the true mean number of miles driven by all truckers? 4. The average score of 64 teenage boys playing a computer game was 100,000 with a standard deviation of 15,000. What is the 95% confidence interval for the true mean score of all teenage boys? 5. The average number of mosquitos caught by 64 mosquito traps was 900 with a standard deviation of 100. What is the 99% confidence interval for the true mean number of mosquitos caught by all mosquito traps? 6. A study of 100 apple trees showed that the average number of apples per tree was The standard deviation of the population is 150. Which of the following is the 95% confidence interval for the mean number of apples for all trees? A) (1975.3, ) B) (1970.6, ) C) (1967.7, ) D) (1965.1, ) Version 2 Page 1
2 7. A study of 60 professors showed that the time they spent on the average in creating test questions was 17.0 minutes per question. The standard deviation of the population is 2. Which of the following is the 98% confidence interval for the average number of minutes it takes to create a test question? A) (15.99, 18.01) B) (16.58, 17.42) C) (16.40, 17.60) D) (12.35, 21.65) 8. If a population has standard deviation 18, what is the minimum sample size to be 95% confident that the error should be accurate to within 4? A) 153 B) 9 C) 78 D) A previous study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 99% confidence interval for the average weight of a nickel. ow many nickels does he need to weigh to be accurate within 15 milligrams? A) 100 B) 666 C) 955 D) squirrels were found to have an average weight of 10.5 ounces with a sample standard deviation is Find the 95% confidence interval of the true mean weight. A) (10.25, 10.75) B) (9.53, 11.47) C) (10.23, 10.77) D) (10.39, 10.61) 11. A food snack manufacturer samples 9 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 9.6 and the sample standard deviation is 0.20, find the 95% confidence interval of the true mean. A) (9.53, 9.67) B) (9.14, 10.06) C) (9.47, 9.73) D) (9.45, 9.75) Version 2 Page 2
3 12. A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000? 13. A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet? A) < p < B) < p < C) < p < D) < p < A random sample of 80 voters found that 46% were going to vote for a certain candidate. Find the 95% limit for the population proportion of voters who will vote for that candidate. A) 35.1% < p < 56.9% B) 36.0% < p < 56.0% C) 36.8% < p < 55.2% D) 40.5% < p < 51.5% 15. The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered cheese pizza. What is the 99% confidence interval of the true proportion of customers who order only cheese pizza? A) < p < B) < p < C) < p < D) < p < In a study of 100 new cars, 29 of them were white. Find ˆp and ˆq where ˆp is the proportion of new cars that is white. A) ˆp =0.29, ˆq =0.29 B) ˆp =0.29, ˆq =0.71 C) ˆp =0.71, ˆq =0.29 D) ˆp =0.71, ˆq = A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company to within 2.5%. A sample of 300 components showed that 20 were defective. ow large a sample is needed to estimate the true proportion of defective components with 99% confidence? Version 2 Page 3
4 18. A report states that 46% of home owners had a vegetable garden. ow large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 5% with 95% confidence? A) 96 B) 191 C) 382 D) A college believes that 28% of applicants to that school have parents who have remarried. ow large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3% with 95% confidence? A) 287 B) 861 C) 1292 D) Is the statement 0 : = 9 a valid null hypothesis? A) Yes, this is a statement that compares a parameter to a value B) Yes, this is a statement that compares two parameters C) No, equalities are not permitted in a null hypothesis D) No, there is no parameter contained in this statement 21. Is the statement 0 : µ = 6 a valid null hypothesis? A) Yes, this is a statement that compares a parameter to a value B) Yes, this is a statement that compares two parameters C) No, equalities are not permitted in a null hypothesis D) No, there is no parameter contained in this statement Version 2 Page 4
5 22. Are the following statements 0 : = 12 A : 12 a valid pair of null and alternative hypotheses? A) No, there are no parameters contained in these statements B) No, the alternative hypothesis cannot contain numeric values C) Yes, these statements are two nonoverlapping hypotheses and compare two parameters D) Yes, these statements are two nonoverlapping hypotheses and compare a parameter to a value 23. Are the following statements 0 : µ 6 A : µ 19 a valid pair of null and alternative hypotheses? A) No, there are no parameters contained in these statements B) No, the alternative hypothesis cannot contain numeric values C) No, these statements have overlapping regions D) No, these statements both compare a parameter to a value 24. For the conjecture, "The average age of students in this class is 21," the null hypothesis is: A) We accept the hypothesis that the average age of students in this class is 21 B) The average age of students in this class is 21 C) The average age of students in this class is not 21 D) We reject the hypothesis that he average age of students in this class is For the conjecture, "The average rent of an apartment is more than $900 per month," the alternative hypothesis is: A) The average rent of an apartment is less than or equal to $900 per month. B) The average rent of an apartment is greater than $900 per month. C) We accept the hypothesis that the average rent of an apartment is more than $900 per month. D) We reject the hypothesis that the average rent of an apartment is more than $900 per month. 26. Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7. A sample of 50 servings of popcorn yields an average of 78 calories. Check Dr. Cuttleman's claim at α = Version 2 Page 5
6 27. At a certain university, the average cost of books per student was $390 per student last semester. In a sample of 60 students this semester, their average cost was $425 with a standard deviation of $75. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis? A) 0.47 B) 0.58 C) 3.61 D) In a particular city, the average salary of secretaries is $29,000 per year. Secretaries at Company A claim that they are paid less than the city average. In a sample of 50 secretaries, their average salary was $25,000 per year with a standard deviation of $5,000. What is the test value for this hypothesis? A) 5.66 B) 0.80 C) 0.80 D) 5.66 Version 2 Page 6
7 Answer Key 1. C 2. B < µ < (96,325, 103,675) 5. (868, 932) 6. B 7. C 8. C 9. B 10. A 11. D < p < B 14. A 15. A 16. B C 19. B 20. D 21. A 22. A 23. C 24. B 25. A : µ = 75 1: µ 75; Critical Values: ± 1.96; z = 3.03 number of calories of popcorn is not C 28. A Reject 0. It appears that the average Version 2 Page 7
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