Question

(please type the answers)(data analysis for decision making 5120)

2. What are the different scales of measurement? Why are scales important in Statistics? 3. Briefly explain descriptive and inferential statistics. 4. Briefly explain the process of statistical inference. Give an example.

Answer 1

A)

• In statistics, there are four data measurement scales: nominal, ordinal, interval and ratio.
• nominal variables are used to “name,” or label a series of values.  
• Ordinal scales provide good information about the order of choices, such as in a customer satisfaction survey.  
• Interval scales give us the order of values + the ability to quantify the difference between each one.  
• Ratio scales give us the ultimate–order, interval values, plus the ability to calculate ratios since a “true zero” can be defined.

B)

• Scales of measurement refer to ways in which variables/numbers are defined and categorized.
• Each scale of measurement has certain properties which in turn determines the appropriateness for use of certain statistical analyses.

C)

• Descriptive statistics uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables.
• Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question

D)

The procedure involved in inferential statistics are:

Begin with a theory

• Create a research hypothesis
• Operationalize the variables
• Recognize the population to which the study results should apply
• Formulate a null hypothesis for this population
• Accumulate a sample of children from the population and continue the study
• Conduct statistical tests to see if the collected sample properties are adequately different from what would be expected under the null hypothesis to be able to reject the null hypothesis

• An example of statistical inference is given below.

Question: From the shuffled pack of cards, a card is drawn. This trial is repeated for 400 times, and the suits are given below:

Suit    Spade    Clubs    Hearts    Diamonds

No.of times drawn    90    100    120    90

While a card is tried at random, then what is the probability of getting a

• Diamond cards
• Black cards
• Except for spade

Solution:

By statistical inference solution,

Total number of events = 400

i.e.,90+100+120+90=400

(1) The probability of getting diamond cards:

Number of trials in which diamond card is drawn = 90

Therefore, P(diamond card) = 90/400 = 0.22

(2) The probability of getting black cards:

Number of trials in which black card showed up = 90+100 =190

Therefore, P(black card) = 190/400 = 0.48

(3) Except for spade

Number of trials other than spade showed up = 90+100+120 =310

Therefore, P(except spade) = 310/400 = 0.78