Section 14.2 Exercises

CLARIFYING THE CONCEPTS

Question 14.9

1. The sign test for the median represents an alternative to which parametric hypothesis test? (p. 14-5)

Question 14.10

2. The key concept for performing the sign test for the median involves converting each of the data values to what? (p. 14-6

14-16

Question 14.11

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

Question 14.12

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

Question 14.13

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

Question 14.14

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

Question 14.15

7. The matched-pair sign test represents an alternative to which parametric hypothesis test? (p. 14-10

Question 14.16

8. The sign test for binomial data represents a special case of which parametric hypothesis test? (p. 14-12

PRACTICING THE TECHNIQUES

image 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:

  1. Use Appendix Table I to find the value of .
  2. State the rejection rule.
  3. Calculate .
  4. Provide the conclusion and the interpretation of the hypothesis test.

Question 14.17

9. vs. , . There are 10 pluses and 10 minuses.

Question 14.18

10. vs. , . There are 2 pluses and 16 minuses.

Question 14.19

11. vs. , . There are 0 pluses and 8 minuses. Two data values equal 0.

Question 14.20

12. vs. , . There is 1 plus and 1 minus. Three data values equal 98.6.

Question 14.21

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

Question 14.22

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

Question 14.23

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

Question 14.24

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:

  1. State the hypotheses.
  2. Find the critical value and state the rejection rule.
  3. Calculate the value of the test statistic .
  4. State the conclusion and the interpretation.

Question 14.25

17. vs. , . There are 100 pluses and 10 minuses.

Question 14.26

18. vs. , . There are 20 pluses and 180 minuses.

Question 14.27

19. vs. , . There are 225 pluses and 5 minuses, and ten data values equal −0.25.

Question 14.28

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:

  1. State the hypotheses.
  2. Find the critical value and state the rejection rule.
  3. Find the value of the test statistic.
  4. State the conclusion and the interpretation.

Question 14.29

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

Question 14.30

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

Question 14.31

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

Question 14.32

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

14-17

For Exercises 25 and 26, perform the sign test for binomial data.

Question 14.33

25. A sample of size has successes. Test whether the population proportion is less than 0.5, using level of significance .

Question 14.34

26. A sample of size has successes. Test whether the population proportion is greater than 0.5, using level of significance .

APPLYING THE CONCEPTS

Question 14.35

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

Question 14.36

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

Question 14.37

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

Question 14.38

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

Question 14.39

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

Question 14.40

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
Facebook $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
Table 14.25: Source: NASDAQ.com

Question 14.41

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 .

14-18

Question 14.42

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 .