CLARIFYING THE CONCEPTS
1. The sign test for the median represents an alternative to which parametric hypothesis test? (p. 14-5)
2. The key concept for performing the sign test for the median involves converting each of the data values to what? (p. 14-6
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3. True or false: In the sign test for the median, if there is a preponderance of plus signs to minus signs, or vice versa (depending on the form of the hypothesis test), then this is evidence against the null hypothesis. (p. 14-6
4. In the sign test for the population median, explain why the sample size for the hypothesis test may not be the same as the number of data values in the sample. (p. 14-6
5. True or false: When computing the test statistic for the large-sample case for the sign test for the population median, we need not calculate . (p. 14-8
6. True or false: The matched-pair sign test is interested in the exact value of the difference between the first and second variables. (p. 14-10
7. The matched-pair sign test represents an alternative to which parametric hypothesis test? (p. 14-10
8. The sign test for binomial data represents a special case of which parametric hypothesis test? (p. 14-12
PRACTICING THE TECHNIQUES
CHECK IT OUT!
To do | Check out | Topic |
---|---|---|
Exercises 9–16 | Example 3 | Small-sample sign test for the population median |
Exercises 17–20 | Example 4 | Large-sample sign test for the population median |
Exercises 21–24 | Example 5 | Sign test for matched-pair data from two dependent samples |
Exercises 25–26 | Example 7 | Sign test for binomial data |
For Exercises 9–16, perform the small-sample sign test for the population median. Use the following steps:
9. vs. , . There are 10 pluses and 10 minuses.
10. vs. , . There are 2 pluses and 16 minuses.
11. vs. , . There are 0 pluses and 8 minuses. Two data values equal 0.
12. vs. , . There is 1 plus and 1 minus. Three data values equal 98.6.
13. Test whether the population median is less than 10, using level of significance .
10 | 8 | 9 | 5 | 11 | 10 | 6 | 9 | 3 | 12 | 1 | 7 | 2 |
14. Test whether the population median is greater than 100, using level of significance .
105 | 219 | 100 | 136 | 345 | 996 | 100 | 400 | 102 | 100 | 229 | 331 |
15. Test whether the population median is less than 400, using level of significance .
105 | 219 | 100 | 136 | 345 | 996 | 100 | 400 | 102 | 100 | 229 | 331 |
16. Test whether the population median differs from 1000, using level of significance .
950 | 1000 | 975 | 925 | 900 | 1000 | 1025 | 900 |
875 | 950 | 1000 | 975 | 925 | 750 | 775 | 900 |
For Exercises 17–20, perform the large-sample sign test for the population median. Use the following steps:
17. vs. , . There are 100 pluses and 10 minuses.
18. vs. , . There are 20 pluses and 180 minuses.
19. vs. , . There are 225 pluses and 5 minuses, and ten data values equal −0.25.
20. vs. , . There are 10,350 pluses and 5,492 minuses, and 300 data values equal 75.
For Exercises 21–24, you are given matched-pair data and are asked to perform a hypothesis test. Assume that each sample of differences is obtained through dependent random sampling. Do the following:
21. Test whether the population mean of the differences , using level of significance .
Subject | 1 | 2 | 3 | 4 | 5 |
Sample 1 | 3.0 | 2.5 | 3.5 | 3.0 | 4.0 |
Sample 2 | 2.5 | 2.5 | 2.0 | 2.0 | 1.5 |
22. Test whether the population mean of the differences , using level of significance .
Subject | 1 | 2 | 3 | 4 | 5 | 6 |
Sample 1 | 10 | 12 | 9 | 14 | 15 | 8 |
Sample 2 | 8 | 11 | 10 | 12 | 14 | 9 |
23. Test whether the population mean of the differences , using level of significance .
Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Sample 1 | 20 | 25 | 15 | 10 | 20 | 30 | 15 |
Sample 2 | 30 | 30 | 20 | 20 | 25 | 35 | 25 |
24. Test whether the population mean of the differences , using level of significance .
Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Sample 1 | 1.5 | 1.8 | 2.0 | 2.5 | 3.0 | 3.2 | 4.0 |
Sample 2 | 1.0 | 1.7 | 2.1 | 2.0 | 2.7 | 2.9 | 3.3 |
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For Exercises 25 and 26, perform the sign test for binomial data.
25. A sample of size has successes. Test whether the population proportion is less than 0.5, using level of significance .
26. A sample of size has successes. Test whether the population proportion is greater than 0.5, using level of significance .
APPLYING THE CONCEPTS
electricmiles
27. Electric Cars. The accompanying table shows the miles-per-gallon equivalent (MPGe) for five electric cars, as reported by www.hybridcars.com in 2014. Test whether the population median mileage is greater than 90 MPGe, using level of significance .
Electric vehicle | Mileage (mpg) |
---|---|
Tesla Model S | 89 |
Nissan Leaf | 99 |
Ford Focus | 105 |
Mitsubishi i-MiEV | 112 |
Chevrolet Spark | 119 |
georgiarain
28. A Rainy Month in Georgia? The following table represents the total rainfall (in inches) for the month of February 2011 for a random sample of 10 locations in Georgia. Test whether the population median amount of rainfall differs from 4 inches, using level of significance .
Location | Rainfall (inches) |
Location | Rainfall (inches) |
---|---|---|---|
Athens | 4.72 | Atlanta | 4.25 |
Augusta | 4.31 | Cartersville | 3.03 |
Dekalb | 2.96 | Fulton | 4.36 |
Gainesville | 4.06 | Lafayette | 3.75 |
Marietta | 3.20 | Rome | 3.26 |
deepwaterclean
29. Deepwater Horizon Cleanup Costs. The following table represents the amount of money disbursed by BP to a random sample of six Florida counties, for cleanup of the Deepwater Horizon oil spill, in millions of dollars. Test whether the population median cleanup cost exceeds $500,000, using level of significance .
County | Cleanup costs ($ millions) |
County | Cleanup costs ($ millions) |
---|---|---|---|
Broward | 0.85 | Pinellas | 1.15 |
Escambia | 0.70 | Santa Rosa | 0.50 |
Franklin | 0.50 | Walton | 1.35 |
carprice
30. New Car Prices. Kelley's Blue Book (www.kbb.com) publishes data on new and used cars. The following table contains the fair market value for five new 2013 and 2014 vehicles (data recorded July 2014). Test whether prices have risen. That is, test whether the population median of the difference in price is greater than zero, using level of significance .
Toyota Camry |
Honda Civic |
Ford 150 |
Chevy Corvette |
Tesla Model S |
|
---|---|---|---|---|---|
2014 (Sample 1) |
$20,672 | $17,069 | $24,362 | $45,684 | $68,738 |
2013 (Sample 2) |
$20,284 | $16,499 | $22,674 | $44,021 | $68,674 |
waterlootemp
31. High and Low Temperatures. The University of Waterloo Weather Station tracks the daily low and high temperatures in degrees Celsius in Waterloo, Ontario, Canada. The table contains a random sample of the daily high and low temperatures for 10 days in calendar year 2010. Test whether the population median of the difference in price differs from zero, using level of significance .
Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
High | 9.4 | 6.1 | 5.9 | 29.1 | 11.9 | 30.6 | 23.1 | 33.1 | 14.8 | 0.1 |
Low | 0.8 | −8.9 | −1.3 | 19.3 | 6.7 | 21.5 | 10.5 | 18.7 | 7.4 | −9.9 |
nasdaq72814
32. NASDAQ Stock Prices. The table provides the start-of-trading and end-of-trading prices for the eight most active stocks on July 28, 2014. Test whether the population median of the difference in price differs from zero, using level of significance .
Stock | End-of- trading price |
Start-of- trading price |
---|---|---|
Sirius XM | $3.38 | $3.44 |
Apple | $99.02 | $97.67 |
$74.92 | $75.19 | |
Micron Technology | $31.98 | $33.42 |
Dollar Tree | $54.87 | $54.22 |
Intel | $34.23 | $34.25 |
Microsoft | $43.97 | $44.50 |
Cisco Systems | $25.92 | $25.97 |
33. Firefox Market Share. A random sample of 1000 Internet users in Finland showed that 472 used the Firefox browser.2 Use the sign test to test whether the population proportion of Internet users in Finland using Firefox differs from 0.50, using level of significance .
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34. Too Much Info on Facebook? A random sample of 287 corporate employees found 189 who worried that work colleagues and employees are sharing too much information on Facebook.3 Use the sign test to test whether the population proportion of corporate employees who worry about this exceeds 0.50, using level of significance .