Sales: Packaging The makers of Country Boy Corn Flakes are

Statistical Literacy Of the following random variables, which have only nonnegative values: z, t, chi-square, F?

Statistical Literacy Of the following probability distributions, which are always symmetric: normal, Students t, chi-square, F?

Critical Thinking Suppose you took random samples from three distinct age groups. Through a survey, you determined how many respondents from each age group preferred to get news from T.V., newspapers, the Internet, or another source (respondents could select only one mode). What type of test would be appropriate to determine if there is sufficient statistical evidence to claim that the proportions of each age group preferring the different modes of obtaining news are not the same? Select from tests of independence, homogeneity, goodness-of- fit, and ANOVA.

Critical Thinking Suppose you take a random sample from a normal population and you want to determine whether there is sufficient statistical evidence to claim that the population variance differs from a corresponding variance speci- fied in a government contract. Which type of test is appropriate, a test of one variance or a test of two variances?

Sales: Packaging The makers of Country Boy Corn Flakes are thinking about changing the packaging of the cereal with the hope of improving sales. In an experiment, five stores of similar size in the same region sold Country Boy Corn Flakes in different-shaped containers for 2 weeks. Total packages sold are given in the following table. Using a 0.05 level of significance, shall we reject or fail to reject the hypothesis that the mean sales are the same, no matter which shape box is used?

Education: Exams Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

Tires: Blowouts A consumer agency is investigating the blowout pressures of Soap Stone tires. A Soap Stone tire is said to blow out when it separates from the wheel rim due to impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 30 Soap Stone tires were inflated to the recommended pressure, and then forces measured in foot-pounds were applied to each tire (1 foot-pound is the force of 1 pound dropped from a height of 1 foot). The customer complaint is that some Soap Stone tires blow out under smallimpact forces, while other tires seem to be well made and dont have this fault. For the 30 test tires, the sample standard deviation of blowout forces was 1353 foot-pounds. (a) Soap Stone claims its tires will blow out at an average pressure of 20,000 foot-pounds, with a standard deviation of 1020 foot-pounds. The average blowout force is not in question, but the variability of blowout forces is in question. Using a 0.01 level of significance, test the claim that the variance of blowout pressures is more than Soap Stone claims it is. (b) Find a 95% confidence interval for the variance of blowout pressures, using the information from the random sample.

Computer Science: Data Processing Anela is a computer scientist who is formulating a large and complicated program for a type of data processing. She has three ways of storing and retrieving data: CD, tape, and disks. As an experiment, she sets up her program in three different ways: one using CDs, one using tape, and the other using disks. Then four test runs of this type of data processing are made on each program. The time required to execute each program is shown in the following table (in minutes). Use a 0.01 level of significance to test the hypothesis that the mean processing time is the same for each method.

Teacher Ratings: Grades Professor Stone complains that student teacher ratings depend on the grade the student receives. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who gives bad grades gets bad ratings. To test this claim, the Student Assembly took a random sample of 300 teacher ratings on which the students grade for the course also was indicated. The results are given in the following table. Test the hypothesis that teacher ratings and student grades are independent at the 0.01 level of significance.

Packaging: Corn Flakes A machine that puts corn flakes into boxes is adjusted to put an average of 15 ounces into each box, with standard deviation of 0.25 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.38 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)

Sociology: Age Distribution A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 20% were under 20 years old, 15% were in the 20- to 35-year-old bracket, 30% were between 36 and 50, 25% were between 51 and 65, and 10% were over 65. A study done this year used a random sample of 210 residents. This sample showed Under 20 2035 3650 5165 Over 65 26 27 69 68 20 At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

Engineering: Roller Bearings Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21 roller bearings from the old manufacturing process showed the sample variance of diameters to be s 2 0.235. Another random sample of 26 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s 2 0.128. Use a 5% level of significance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.

Engineering: Light Bulbs Two processes for manufacturing 60-watt light bulbs are under study. In both cases, the life (in hours) of the bulb before it burns out is being examined. A random sample of 18 light bulbs manufactured using the old process showed the sample variance of lifetimes to be s 2 51.87. Another random sample of 16 light bulbs manufactured using the new process showed the sample variance of the lifetimes to be s 2 135.24. Use a 5% level of signifi- cance to test the claim that the population variance of lifetimes for the new manufacturing process is larger than that of the old process.

Advertising: Newspapers Does the section in which a newspaper ad is placed make a difference in the average daily number of people responding to the ad? Is there a difference in average daily number of people responding to the ad if it is placed in the Sunday newspaper as compared with the Wednesday newspaper? Video Entertainment is a video club that sells videotapes featuring movies of all kindsinstructional videos, videos of TV specials, etc. To attract new customers, Video Entertainment ran ads in the Wednesday newspaper and in the Sunday newspaper offering six free videotapes or DVDs to new members. In addition, the ads were placed in the sports section, the entertainment section, and the business section of the local newspaper. Ads running in the different sections carried different promotion codes. Different codes also were used for Wednesday ads compared with Sunday ads. The numbers of people responding to the ads for days selected at random were recorded according to the promotion codes. The results follow: (a) List the factors and the number of levels for each factor. (b) Use the following Minitab printout and the F distribution table (Table 8 of Appendix II) to test for interaction between the variables. Use a 1% level of significance. Section of Newspaper Day Sports Entertainment Business Wed 12 15 11 22 14 17 2 4 3 12 15 20 22 18 12 5 0 1 Sun 20 23 25 32 26 28 13 16 13 33 15 17 31 25 41 15 14 10 Minitab Printout for Mean Number of Responses per Day Analysis of Variance for Response Source DF SS MS F P Day 1 1024.0 1024.0 55.28 0.000 Section 2 1573.6 786.8 42.48 0.000 Interaction 2 38.0 19.0 1.03 0.371 Error 30 555.7 18.5 Total 35 3191.2 (c) If there is no evidence of interaction between the factors, test for a difference in mean number of daily responses for the levels of the day factor. Use a 0.01. (d) If there is no evidence of interaction between the factors, test for a difference in mean number of daily responses for the levels of the section factor. Use a 0.01.