Basic Statistics Self Assessment Test

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1 Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A soda-dispensing machine fills 12-ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation of.02 ounce. 1. What is the probability that a randomly selected soda contains less than 12 ounces? a. Approximately 1.0 b..5 c. Approximately 0 d What proportion of the soda cans contain between ounces and ounces of soda? a b c d The plant manager wants to know the amount at which 98.5% of the sodas contain more soda. Help him find this value. a ounces b ounces c ounces d ounces

2 PAGE 2 A beer company has two objectives: A) To make profits B) To make sure advertising is not misleading To accomplish objective A, the company requires that no more than.2% of their 12 ounce bottles of beer contain more than 12.1 ounces. To accomplish objective B, the company requires that at least 97.5% of their bottles of beer contain more than 12 ounces. The amount of beer dispensed by the filling machine has a normal distribution with a standard deviation of.01 ounces. The company can set the value of the mean on the machine. 4. What setting should the company use for the mean to meet objective A? a. 12 ounces b. < or = ounces c. < or = ounces d. < or = 12 ounces e. Not enough information. 5. What setting should the company use for the mean to meet objective B? a. = or > 12 ounces b. = or > ounces c. = or > ounces d. = or > ounces e. Not enough information. Most copy machines are basically the same. For companies to succeed in the copy industry, they must sell service to their customers. Suppose Xerox claims that one particular copy machine has a distribution of lifetimes that has a mean of 10,000 copies and a standard deviation of 1250 copies. 6. If we sampled 100 of this type of copy machine, find the probability that the sample mean lifetime would exceed 10,250 copies. a b c d..4207

3 PAGE 3 7. Find the probability that the sample mean of the 100 copy machines will fall between 9,000 and 10,125 copies. a b c d A study in 1984 indicated that the cost of hiring an employee (excluding salary) ranges from about $1500 for an entry-level secretary to more than $40,000 for a manager. In order to estimate its mean cost of hiring an entry-level secretary, a large corporation samples eight of the entry-level secretaries it had hired during The cost (in dollars) involved in their hirings resulted in a sample mean of $ and a sample standard deviation of $ Find a 95% confidence interval for µ. a or b or c or d or Suppose the interval turned out to be ($ , $ ). Which of the following statements regarding the 1984 study can be made? a. Based on the interval, we believe the $1500 value mentioned by the 1984 study is 95% reliable in b. We are 95% confident the mean cost of hiring an entry-level secretary in 1991 exceeds the $1500 value stated by the 1984 study. c. We are 95% confident the mean cost of hiring an entry-level secretary in 1991 is less than the $1500 value stated in the 1984 study. 10. Which of the following assumptions are not necessary for this analysis to be valid? a. The population of hiring costs of entry-level secretaries is normally distributed. b. The sample mean cost is normally distributed. c. The eight secretary hiring costs were randomly sampled. d. All are necessary assumptions.

4 PAGE 4 A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is ounces and the standard deviation is.2 ounces. 11. Which of the following is the set of hypotheses the company wishes to test? a. H 0 : µ < 12 vs. Ha: µ = 12 b. H 0 : µ = 12 vs. Ha: µ > 12 c. H 0 : µ = 12 vs. Ha: µ < 12 d. H 0 : µ = 12 vs. Ha: µ not = Calculate the appropriate test statistic. a. t = b. t = 0.50 c. t = d. t = Using α =.05 and a two-tailed test, find the appropriate rejection region. a. Reject H 0 if t > or t < b. Reject H 0 if t > or t < c. Reject H 0 if t > or t < d. Reject H 0 if t > or t < Suppose the p-value for this test turned out to be Which of the following is correct? a. At α =.05, reject the null hypothesis. b. At α =.075, accept the null hypothesis. c. At α =.085, fail to reject the null hypothesis. d. At α =.095, reject the null hypothesis. 15. Suppose the test results indicated the null hypothesis should be rejected and, as a result, the company shut down their machine for inspection. A thorough examination revealed that the machine was filling the bottles correctly. From a statistical point of view, which of the following is true? a. A correct decision was made. b. Both a Type I and Type II errors were made. c. A Type II error was made. d. A Type I error was made.

5 PAGE 1 ANSWER KEY FOR TEST- Basic Statistics Self Assessment Test 1. c 2. b 3. b 4. b 5. c 6. b 7. a 8. c 9. b 10. b 11. c 12. a 13. b 14. d 15. d

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