BUS/ST 350 Exam 3 Spring 2012

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1 BUS/ST 350 Exam 3 Spring 2012 Name Lab Section ID # INSTRUCTIONS: Write your name, lab section #, and ID# above. Note the statement at the bottom of this page that you must sign when you are finished with the exam. Supply the following information on SIDE ONE of the scantron sheet: Enter your name (last name first!) in the "name" section; no nicknames! FILL IN THE BUBBLES. Enter your 3 digit lab section number in the "special code" section. FILL IN THE BUBBLES. Enter your student identification number in the "identification number" section. FILL IN THE BUBBLES. IMPORTANT! BUBBLE IN the version number (either "1", "2"or "3") of your copy of the exam in the section marked "GRADE OR EDUCATION". There are 18 multiple choice questions. On the test circle the letter that corresponds to the answer you select. Also indicate your selection on the opscan sheet. Use a #2 pencil! For each wrong answer 5 points will be subtracted from 100. When you are finished: separate your scantron sheet from the test! i) place the 1st page of your test in the proper lab section stack on the stage ii) place your scantron sheet in the folder labeled with your version of the test. GOOD LUCK!! Statement of academic honesty: I have neither given assistance to another student nor received assistance from another student while taking this exam. Signed 1

2 Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 400 policyholders is selected. 1) The probability that the sample proportion of policyholders filing claims involving theft or robbery from their homes is less than 8% is A) B) C) D) E) ) The width of a confidence interval estimate for a proportion will be A) wider for a sample size of 100 than for a sample size of 50. B) narrower when the sample proportion is 0.50 than when the sample proportion is C) narrower for 90% confidence than for 95% confidence. D) narrower for 99% confidence than for 95% confidence. 3) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers.. The resulting 90% confidence interval for the proportion p of college students that prefer American cars is (0.332, 0.460). Which of the following is a correct interpretation of the interval? A) 90% of all college students prefer American cars between.332 and.460 of the time. B) We are 90% confident that the proportion p of all college students who prefer American cars falls between.332 and.460. C) We are 90% confident that the interval (0.332, 0.460) contains the true proportion p of all college students who prefer American cars. D) We are 90% confident that the sample proportion of the 159 sampled students who prefer American cars falls between.332 and.460. E) Between and of American cars are preferred by college students. 4) In one region of the country, the distribution of September energy consumption for single-family homes can be described by a normal model with mean 1050 kwh and standard deviation 218 kwh. Find the 33rd percentile of the consumption level, that is, find the consumption level separating the bottom 33% from the top 67%. A) B) C) D) ) The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $7500? A) B) C) D) ) In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system to a semester-system. How many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval? No information is available concerning an approximate value of p. A) 114 B) 182 C) 261 D) 206 7) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 99% confidence interval to estimate the true proportion of students on financial aid. A) 0.59 ± B) 0.59 ± C) 0.59 ± D) 0.59 ± 0.003

3 8) Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0 < z < k) = , find the value of k. A) 0.61 B) C) 1.76 D) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 9) A) B) C) D) ) Five years ago at a large university the proportion of business major that were female was Using the information above, what total size sample would be necessary if we wanted to estimate the current true proportion to within ±0.08 using 95% confidence? A) 105 B) 597 C) 420 D) ) In New York City 36% of adults in the city have credit card debts of more than $2000. A simple random sample of n = 100 adults is obtained from New York City. Describe the sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000. A) Approximately normal; E(p) = 36, SD(p) = 4.8 B) Approximately normal; E(p) = 0.36, SD(p) = C) Binomial; E(p) = 36, SD(p) = 4.80 D) Approximately normal; E(p) = 0.36, SD(p) = ) We have calculated a confidence interval based on a sample of size n = 100. Now we want a new interval with the same level of condfidence but with a margin of error that is only one-fourth as large. How large does our new sample need to be? A) 200 B) 25 C) 400 D) 50 E) ) The manager at a local movie theater has collected data for a long period of time and has concluded that the distribution of revenue from concession sales during the first show each evening can be described by a normal model with mean $ and standard deviation $80. Based on this information, what is the probability that the revenue on the first show will be between $300 and $500? A) B) C) D) ) A P-value indicates A) the probability that the null hypothesis is true. B) the probability of obtaining a value of the test statistic as extreme or more extreme than what we obtained, given that the alternative hypothesis is true C) the probability that the alternative hypothesis is true. D) the probability of obtaining a value of the test statistic as extreme or more extreme than what we obtained, given that the null hypothesis is true. E) The probability that we have made a mistake.

4 Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 15) Shaded area is A) 1.26 B) 1.39 C) 1.48 D) ) The distribution of the volume of soda in quart soda bottles can be described by a normal model with mean 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz? A) B) C) D) ) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 32.3% of them plan to go into general practice. The approximate P-value for the test H0: p = 0.28, Ha: p > 0.28 of the school's claim is A) B) C) D) ) A truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which hypotheses should they test? A) H0: p = 0.98 HA: p > 0.98 B) H 0 : p = 0.98 HA: p < 0.98 C) H0: p = 0.98 HA: p < 0.98 D) H0: p > 0.98 HA: p = 0.9 E) H 0 : p = 0.98 HA: p > 0.98

5 ANSWERS: 1. D 2. C 3. C 4. D 5. B 6. D 7. B 8. C 9. C 10. D 11. B 12. E 13. D 14. D 15. C 16. B 17. B 18. C

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