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Inferential or Descriptive Statistics

I. What level of data?

Question: If statisticians were planning a study on the levels of measurement, how would they identify numbers associated with the example below?

(a)scores on a teacher-prepared math test __________________________

(b)scores on a commercially prepared standardized reading test_____________

(c) salaries of coal miners_____________________________________

(d) all numeric vehicle license plates ________________________________

(e)class ranks for graduating high school seniors ______________________

II. Discrete or Continuous Data?

Question: If numbers were associated with each of these examples below, what kind of numbers would they be?

(a)heights in feet of seventh-grade boys _______________________________

(b)depths of the Atlantic Ocean _______________________________________

(c)people at a rock concert ___________________________________________

(d)tax returns for auditing ____________________________________________

(e)mass produced cigarettes ___________________________________________

III.Inferential or Descriptive Statistics?

Read the scenarios, and identify which kind of statistics is referenced.

(a)a pharmaceutical company testing a new drug to treat insomnia to see whether it is superior to its predecessor
______________________________________

(b)a television anchor's report on the possible number of whales in the Pacific Ocean

________________________________________

(c)a television poll that reveals political preferences of residents of Alaska

_________________________________________

(d)a laboratory study regarding which fertilizer is best among five for growing mushrooms

__________________________________________

(e)a newspaper story about the number of condominiums to be constructed in a planned high rise building

__________________________________________

IV. Identify which one of the examples in Part III above best represents hypothesis testing. Explain why you selected that particular example.

V.Which type of Sampling?

Identify the type and explain why you selected that choice rather than the other options (2 pts choice/3 points justification).

(a)Consumer Research Company sends its employees to randomly selected gasoline stations throughout the nation to report on prices per gallon.

(b) Political Analysis, Inc. divides the USA into a number of different regions. Then, the research personnel randomly select 100 to 1000 adults from each of those regions to investigate the peoples' choice for president in 2008. Size of the region dictates whether a larger number or a smaller number of people will be sampled.

Solution Preview

I. What level of data?
There are four type of measurement levels i.e. scales.
 Nominal scale: It is a figurative labeling scheme where numbers are labels or tags for identifying and classifying the objects. Example - Roll numbers assigned to students
Ordinal scale: The numbers assigned are ranks to indicate the relative extent to which each object possesses some characteristics. Example - Ranks based on GPA
Interval scale: It represents values of the characteristics, which are numerically equal distant. Example - Performance rating on 0-10 scale
Ratio scale: This scale has got all the properties of above mentioned three scales and can identify objects, rank them, classify them. This scale has the property of absolute zero and the differences between two values are meaningful. Example - Height, weight

Question: If statisticians were planning a study on the levels of measurement, how would they identify numbers associated with the example below?

(a)scores on a teacher-prepared math test __________________________
 This is a ratio level measurement with absolute zero and differences can be compared with meaningful interpretation

(b)scores on a commercially prepared standardized reading test_____________
 In standardized tests relative scores are measured and hence this type of measurement is ordinal level measurement. This measurement can tell you the relative strength of characteristics possessed by the object along with ranks of the objects. However, this measurement will not tell the strength of the difference i.e. the magnitude of the differences between two objects.

(c) salaries of coal miners_____________________________________
 This is clearly ratio level measurement as it is with absolute zero and differences between two salary values can be interpreted meaningfully.

(d) all numeric vehicle license plates ________________________________
 This is nominal level measurement as the number license numbers are used to identify or classify the cars.

(e)class ranks for graduating high school seniors ______________________
 This is ordinal level measurement as ranks suggest relative strength of performance but the differences cannot ...

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