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List of Statistical Techniques
Section* *

#### Estimate a Value

- Estimating a Mean
- Estimating a Proportion
- Estimating the difference of two means
- Estimating a mean with paired data
- Estimating the difference of two proportions

#### Test a hypothesis

- Test about a mean
- Test about a proportion
- Test to compare two means (independent)
- Test to compare two means (paired)
- Test to compare two proportions
- Test about a slope
- Test to compare several means
- Test of Strength & Direction of Linear Relationship of 2 Quantitative Variables
- Test to Compare Two Population Variances

#### Examine a Relationship

- Relationship in a 2-Way Table

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Choose the Correct Statistical Technique
Section* *

#### Directions

For the scenarios below, choose a method that is suitable for the given situation.

**Note:**There is no need to work out the following problems. This is simply an exercise to help you select the appropriate statistical method given the description of a research context. Determine the statistical technique(s) that you think is most appropriate and then click on the 'Inspect' button on the right to compare your answers!

- A survey of National Federation of Independence Business (NFIB) indicates that small businesses intended to increase their hiring as well as their capital expenditures during 1986 as compared with 1985. Suppose that, as part of a follow-up survey by NFIB, 20 small businesses, randomly chosen from the NFIB's list of 2,100 companies, show an average hiring from 1985 equal to 3.2 new employees per firm and a standard deviation of 1.5 hires. A random sample of 30 small businesses taken at the end of 1986 shows an average of 5.1 new hires and a standard deviation of 2.3 hires. At the \(\alpha = 0.01\) level of significance, can you conclude that average hiring by all small businesses in 1986 increased as compared with 1985?
- It is known that the average stay of tourists in Hong Kong hotels has been 3.4 nights. A tourism industry analyst wanted to test whether recent changes in the nature of tourism to Hong Kong have changed from this past average. The analyst obtained the following random sample of the number of nights spent by tourists in Hong Kong hotels: 5, 4, 3, 2, 1, 1, 5, 7, 8, 4, 3, 3, 2, 5, 7, 1, 3, 1, 1, 5, 3, 4, 2, 2, 2, 6, 1, 7. Conduct the test using the 0.05 level of significance.
- There are 155 banks involved in certain international transactions. A federal agency claims that at least 35% of these banks have total assets of over \$10 billion (In U.S. dollars). An independent agency wants to test this claim. It gets a random sample of 50 out of the 155 banks and finds that 15 of them have total assets of over \$10 billion. Can the claim be rejected?
- General Motors Corporation hopes to reduce anticipated production costs of its Saturn Model by instituting an assembly schedule that will reduce average production time to about 40 hours per car. In a test run of the new assembly line, 40 cars are built at a sample average time per car of 46.5 hours and a sample standard deviation of 8.0 hours. A test run of 38 cars using the old assembly schedule results in a sample of mean of 51.2 hours and a sample deviation of 9.5 hours. Is there proof that the new assembly schedule reduces the average production time per car?
- A telephone company wants to estimate the average length of long-distance calls during weekends. A random sample of 50 calls gives a mean \(\bar{X} =14.5\) min and standard deviation
*s*= 5.6 min. Provide an interval estimate for the average length of a long-distance phone call during weekends. - Several companies have been developing electronic guidance systems for cars. Motorola and Germany's Blauounkt are two firms in the forefront of such research. Out of 120 trials of the Motorola model, 101 were successful; and out of 200 tests of the Blaupunkt model, 110 were successful. Is there evidence to conclude that the Motorola electronic guidance system is superior to the German competitor?
- An important measure of the risk associated with a stock is the standard deviation, or variance, of the stock's price movements. A financial analyst wants to test the one-tailed hypothesis that stock A has a greater risk (larger variance of price) than stock B. A random sample of 25 daily prices of stock A gives \(s_{A}^2= 6.52\), and a random sample of 22 daily prices of stock B gives a sample variance of \(s_{B}^2= 3.47\). Carry out the test at \(\alpha = 0.01\).
- A company is interested in offering its employees one of two employee benefit packages. A random sample of the company's employees is collected, and each person in the sample is asked to rate each of the two packages on an overall preference scale of 0 to 100. The order of presentation of each of the two plans is randomly selected for each person in the sample. The paired data are:
- Program A: 45 67 63 59 77 69 45 39 52 58 70 46 60 65 59 80
- Program B: 56 70 60 45 85 79 50 46 50 60 82 40 65 55 81 68

Determine whether the employees rate one package higher.

- Analysis of variance has long been used in providing evidence of the effectiveness of pharmaceutical drugs. Such evidence is required before the FDA will allow a drug to be marketed. In a recent test of the effectiveness of a new sleeping pill, three groups of 25 patients each were given the following treatments. One group was given the drug, the second group was given a placebo, and the third group was given no treatment at all. The results are as follows.
Drug group 12, 17, 34, 11, 5, 42, 18, 27, 2, 37, 50, 32, 12, 27, 21, 10, 4, 33, 63, 22, 41, 19, 28, 29, 8 Placebo group 44, 32, 28, 30, 22, 12, 3, 12, 42, 13, 27, 54, 56, 32, 37, 28, 22, 22, 24, 9, 20, 4, 13, 42, 67 No-treatment group 32, 33, 21, 12, 15, 14, 55, 67, 72, 1, 44, 60, 36, 38, 49, 66, 89, 63, 23, 6, 9, 56, 58, 39, 59 Determine whether or not the drug is effective.

- The maker of portable exercise equipment, designed for the health-conscious people who travel too frequently to use a regular athletic club, wants to estimate the proportion of traveling business people who may be interested in the product. A random sample of 120 traveling business people indicates that 28 of them may be interested in purchasing the portable fitness equipment. Provide an interval estimate for the proportion of all travelling business people who may be interested in the product.
- A study undertaken by Montgomery Securities to access average labor and materials costs incurred by Chrysler and General Motors in building a typical four-door, intermediate-sized car. The reported average cost for Chrysler was \$9500, and for GM it was \$9780. Suppose that these data are based on random samples of 25 cars for each company, and suppose that both standard deviations are equal to \$1500. Test the hypothesis that the average GM car of this type is more expensive to build than the average Chrysler car of the same type.
- Recent studies indicates that in order to be globally competitive, firms must form global strategic partnerships. An investment banker wants to test whether the return on investment for international ventures is different from return on investment for similar domestic ventures. A sample of 12 firms that recently entered into ventures with foreign companies is available. For each firm, the return on investment for both the international venture (I), and similar domestic venture (D) is given:
- D(%): 10 12 14 12 12 17 9 15 8.5 11 7 15
- I(%) : 11 14 15 11 12.5 16 10 13 10.5 17 9 19

Assuming that these firms represent a random sample from the population of all firms involved in global strategic partnerships, can the investment banker conclude that there are differences between average returns on domestic ventures and average returns on international ventures? Explain.

- When new paperback novels are promoted at bookstores, a display is often arranged with copies of the same book with differently colored covers. A publishing house wanted to find out whether there is a dependence between the place where the book is sold and the color of its cover. For one of its latest novels, the publisher sent displays and a supply of copies of the novels to large bookstores in five major cities. The resulting sales of the novel for each city-color combination are as follows. Numbers are in thousands of copies sold over a three-month period.
City Red Blue Green Yellow Total New York 21 27 40 15 103 Washington 14 18 28 8 68 Boston 11 13 21 7 52 Chicago 3 33 30 9 75 Los Angeles 30 11 34 10 84 **Total**79 102 153 49 383 Assume that the data are random samples for each particular color-city combination and that the inference may apply to all novels. Are color and location related?

- Certain eggs are stated to have reduced cholesterol content, with an average of only 2.5% cholesterol. A concerned health group wants to test whether the claim is true. The group believes that more cholesterol may be found, on the average, in the eggs. A random sample of 100 eggs reveals a sample average content of 5.2% cholesterol, and a sample standard deviation of 2.8%. Does the health group have cause for action?
- Two 12-meter boats, the K boat and the L boat, are tested as possible contenders in the America's Cup races. The following data represent the time, in minutes, to complete a particular tack in independent random trials of the two boats.
- K boat: 12.0, 13.1, 11.8, 12.6, 14.0, 11.8, 12.7, 13.5, 12.4, 12.2, 11.6, 12.9
- L boat: 11.8, 12.1, 12.0, 11.6, 11.8, 12.0, 11.9, 12.6, 11.4, 12.0, 12.2, 11.7

Test the null hypothesis that the two boats perform equally well. Is one boat faster, on the average, than the other?