STATISTICS

Instructions: Read each of the following problems, then decide what procedure to follow to properly complete the problem.

 

  1. A Major oil company has developed a new gasoline additive that is supposed to increase mileage. To test that hypothesis, 10 cars are randomly selected. Each car sampled is driven both with and without the additive. The resulting gas mileage, in miles per gallon (mpg), are displayed in the second and third columns of the table.

    2.  

    Car

    With additive

    Without additive

    1

    25.7

    24.9

    2

    20.0

    18.8

    3

    28.4

    27.7

    4

    13.7

    13

    5

    18.8

    17.8

    6

    12.5

    11.3

    7

    28.4

    27.8

    8

    8.1

    8.2

    9

    23.1

    23.1

    10

    10.4

    9.9

    Do the data provide sufficient evidence to conclude that, on the average, the gasoline additive improves gas mileage? Use a = 0.05. A normal probability plot reveals no outliers and is roughly linear.

     

  2. A manufacturer of watches claims that the weekly error made by the watches she produces has a standard deviation of about 1 second. To test that claim, a random sample of 20 watches are set to the correct time. After 1 week, the error made by each watch is recorded. The results, in seconds, are as follows.

    3. 0.6

    2.3

    2.0

    -2.1

    -1.4

    -0.5

    1.5

    -0.3

    0.4

    0.6

    0.4

    -2.2

    0.7

    0.5

    -1.3

    -2.0

    2.6

    -0.8

    1.0

    -0.6

    Can we concluse that the standard deviation, s, of the weekly errors exceeds the 1-second claim made by the manufacturer? Use a = 0.05. (Note: Sx = 1.4 and Sx2 = 39.32.) Assume normal distribution.

     

  3. A random sample of nine custom homes currently listed for sale in the Equestrian Estates provided the following information on size and price. Here x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

X

26

27

33

29

29

34

30

40

22

Y

235

249

267

269

295

345

415

475

195

Do the data provide sufficient evidence to conclude that for custom homes in the Equestrian Estates, size and price are positively linearly correlated? Use a = 0.005. Assume that a population regression line exists, that for any given x the y's are normally distributed, and that the y's have equal standard deviations.

4.  Manufacturers of golf balls always seem to be claining that their ball goes the farthest.  a writer for a sports magazine decided to conduct an impartial test.   She randomly selected 20 golf professionals and then randomly assigned four golfers to each of five brands.  Each golfer drove the assigned brand of ball.  The driving distances, inyards, are displayed in the following table.

Brand 1        Brand 2         Brand 3         Brand 4         Brand 5
    286             279                 270                 284             281
    276             277                 262                 271             293
    281             284                 277                 269             276
    274             288                 280                 275             292

Do the data provide sufficient evidence to conclude that a difference exists in mean driving distances among the five brands of golf ball?  Use a significance level of 0.05.  (Assume that the populations are normally distributed, the samples independent, and equal population standard deviations.)

5.  In 1993 about 62.1 million Americans suffered injuries, as reported by the National Center for Health Statistics in Vital and Health Statistics.  More males (33.4 million) were injured than females (28.7 million).  Those statistics do not tell us whether males and females tend to be injured in similar circumstances.  A random sample of accident reports gave the data in the contingency table below.

                                Male          Female         Total
At work                     18                   4               22
Home                         26                 28              54
Motor vehicle               4                   6               10
Other                         36                 24               60

Total                         84                 62               146

At 0.05 significance level, do the data provide sufficient evidence to conclude that an association exists between accident circumstance and sex? 

Which Procedure Should You Use?