metrics and information excercises

No

(d) Are the data symmetric or skewed? If skewed, which direction? multiple choice 2

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Yes, the data are skewed to the right.

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No, the distribution is symmetric.

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Yes, the data are skewed to the left.

2. How long does it take to fly from Denver to Atlanta on Delta Airlines? The table below shows 56 observations on flight times (in minutes) for the first week of March 2005.

  Click here for the Excel Data File   (a) Fill in the highlighted cells in the table below. (Round your answers to 2 decimal places.)

(b) This distribution appears to be:    multiple choice

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Skewed right

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Skewed left

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Symmetric

3. Caffeine content in a 5-ounce cup of brewed coffee ranges from 60 to 180 mg, depending on brew time, coffee bean type, and grind.   (a) Use the midrange to estimate the measure of centre.   Midrange              (b) Use the Empirical Rule to estimate the standard deviation.   Standard deviation              (c) Why is the assumption of a normal, bell-shaped distribution important in making these estimates?    multiple choice

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Because we can estimate the mean with the midrange.

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Because we can estimate the mean with the standard deviation.

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Because we can estimate the standard deviation with the median.

4. On Professor Hardtack's last cost accounting exam, the mean score was 71, the median was 77, and the mode was 81.   (a) Check the appropriate choice of the distribution, based on the statistics given.    multiple choice

·

The distribution should be skewed to the left because the mean is less than the median.

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The distribution should be skewed to the left because the standard deviation is less than the median.

·

The distribution should be skewed to the right because the mean is less than the median.

·

The distribution should be skewed to the right because the coefficient of variance is less than the median.

(b) Select the factor that might cause the distribution to be like this. (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)    check all that apply

· Many students did not study for the exam

· No students scored a C

· Few students did not study for the exam

· Most students scored a C or higher

5. The U.S. Fisheries and Wildlife Service requires that scallops harvested from the ocean must weigh at least 1/36 pound. The harbormaster at a Massachusetts port randomly selected 18 bags of scallops from 11,000 bags on an arriving vessel. The average scallop weight from the 18 bags was 1/39 pound.   (a) Would the population of 11,000 bags be considered effectively infinite in this case?    multiple choice 1

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Yes

·

No

  (b) Which value represents a sample statistic: 1/36 or 1/39?    multiple choice 2

·

1/36

·

1/39

The U.S. Fisheries and Wildlife Service requires that scallops harvested from the ocean must weigh at least 1/36 pound. The harbormaster at a Massachusetts port randomly selected 18 bags of scallops from 11,000 bags on an arriving vessel. The average scallop weight from the 18 bags was 1/39 pound.   (a) Would the population of 11,000 bags be considered effectively infinite in this case?    multiple choice 1

·

Yes

·

No

  (b) Which value represents a sample statistic: 1/36 or 1/39?    multiple choice 2

·

1/36

·

1/39

6.

  Click here for the Excel Data File   (a) What kind of display is this?   multiple choice 2

·

Scatter chart

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Column chart with 3D visual effect

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Bar chart with 3D visual effect

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Line chart

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Pie chart

  (b-1) Identify its strengths, using the tips and checklists shown in this chapter. (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)   check all that apply 2

· Good title

· Labels on X- and Y-axes

· Measurement included on Y-axis

· No distracting pictures

· Non-zero origin

· Good use of gridlines

· No source

  (b-2) Identify its weaknesses, using the tips and checklists shown in this chapter. (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)   check all that apply 4

· No source

· Large gap between time series due to difference in magnitude

· No title

· Distracting pictures

  (c) Would a different type of display be better?   multiple choice 4

·

Use of logarithmic scale would correct proportion issue

·

2D bar chart with zero origin on X-axis would improve chart

·

Column chart with 3D visual effect would improve the display

7. The average time a Boulder High varsity lacrosse player plays in a game is 29 minutes with a standard deviation of 4 minutes. Nolan’s playing time in last week’s game against Fairview was 48 minutes.   (a) Calculate the z-score for Nolan’s playing time against Fairview. (Round your answer to 2 decimal places.)    Nolan's standardized z-score               (b) By the Empirical Rule, was Nolan’s playing time unusual when compared to the typical playing time?    multiple choice

·

Yes

·

No

8. In fuel economy tests in city driving conditions, a hybrid vehicle’s mean was 46.6 mpg with a standard deviation of 2.7 mpg. A comparably sized gasoline vehicle’s mean was 27.8 mpg with a standard deviation of 3.3 mpg.   Which vehicle’s mpg was more consistent in relative terms? (Round your answers to 1 decimal places.)  

  Which vehicle's mpg was more consistent in relative terms?   multiple choice

·

hybrid

·

Gasoline

9. Would you use a sample or a census to measure each of the following? 

10. In 2007, total compensation (in thousands of dollars) for 40 randomly chosen CEOs ranged from 444 to 18,305, with quartiles Q1 = 9,610, Q2 = 12,275, and Q3 = 15,792.   (a) Select the correct box plot for the given data.  

  multiple choice 1

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BoxPlot A

·

BoxPlot B

·

BoxPlot C

  (b) Describe its shape (skewed left, symmetric, skewed right).   multiple choice 2

·

The distribution is skewed right.

·

The distribution is symmetric.

·

The distribution is skewed left.

11. A small suburban community agreed to purchase police services from the county sheriff’s department. The newspaper said, “In the past, the charge for police protection from the Sheriff’s Department has been based on the median cost of the salary, fringe benefits, etc. That is, the cost per deputy was set halfway between the most expensive deputy and the least expensive.”   (a) Is this the median? If not, what is it?    multiple choice 1

·

No, it is the mean.

·

No, it is the midrange.

·

Yes, it is the median.

  (b) Which would probably cost the city more, the midrange or the median? Why?            cost the city more because it         by outliers.

12. On San Martin Boulevard, embedded sensors kept track of the vehicle traffic count each hour for five weekdays, Monday through Friday, between 6 a.m. and 8 p.m. (5 weeks × 14 hours = 70 observations).  

    (a) Visually estimate the quartiles Q1, Q2, Q3.  

  (b) Estimate xmin and xmax.  

(c) Is the distribution symmetric?   multiple choice

·

No, the distribution is skewed right

·

Yes, the distribution is symmetric

·

No, the distribution is skewed left

13. Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70 judges rated both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the judges tasted Sauce A first, while the other half tasted Sauce B first. Actual results are shown below for “overall liking.”   Sauce A: 6, 7, 9, 3, 7, 6, 7, 2, 6, 7, 3, 6, 6, 6, 5, 3, 6, 6, 6, 7, 7, 6, 1, 6, 7, 5, 1, 7, 6, 7, 5, 8, 6, 1, 6, 5, 8, 6, 1, 5, 6, 5, 5, 5, 2, 6, 6, 8, 8, 5, 6, 8, 1, 8, 5, 8, 7, 5, 7, 6, 2, 9, 5, 6, 6, 8, 8, 8, 5, 3   Sauce B: 8, 5, 6, 7, 6, 9, 8, 8, 8, 5, 6, 3, 8, 5, 6, 5, 8, 7, 7, 5, 7, 2, 7, 5, 9, 5, 8, 7, 9, 6, 7, 5, 6, 5, 7, 6, 6, 8, 5, 5, 5, 5, 7, 7, 5, 5, 3, 5, 8, 6, 7, 5, 7, 5, 8, 8, 5, 8, 3, 6, 5, 6, 7, 5, 3, 6, 6, 8, 6, 8  

  Click here for the Excel Data File   (a) Calculate the mean and standard deviation for each sample. (Round your answers to 3 decimal places.)  

(b) Calculate the coefficient of variation for each sample. (Enter your answer as a percentage rounded to 1 decimal place.)  

(c) What is your conclusion about consumer preferences for the two sauces?    multiple choice

·

On average, consumers seem to prefer Sauce B over Sauce A.

·

On average, consumers seem to prefer Sauce A over Sauce B.

14. Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2744 mm with a standard deviation of 0.000824 mm.   (a) A certain shipment has a diameter of 0.2736. Find the standardized z-score for this shipment. (Round your answer to 3 decimal places.)   z              (b) Is this an outlier?    multiple choice

·

No

·

Yes

15. Bags of jelly beans have a mean weight of 415 gm with a standard deviation of 7 gm.   Use Chebyshev’s Theorem to find a lower bound for the number of bags in a sample of 225 that weigh between 394 and 436 gm.    Lower bound            bags