a) Describe the difference between descriptive statistics and inferential statistics. Illustrate
with an example,
b) A researcher wishes to estimate the proportion of all adults who own a cell phone. He
takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 12984 572
or about 83% own a cell phone.
aæ What is the population of interest?
b. What is the parameter of interest?
c. What is the statistic involved?
d, Based on this sample, do we know the proportion of all adults who own a cell phone?
Explain fully.
Answers
Answer:
The primary difference between descriptive and inferential statistics is that descriptive statistics measure for definitive measurement while inferential statistics note the margin of error of research performed.
researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 1298∕1572≈. 83 or about 83% own a cell phone.
1 - A “population of interest” is defined as the population/group from which a researcher tries to draw conclusions. It is a subset of the general population that the surveyor wants to know more about. Many research studies require specific groups of interest to make decisions based on their findings.
2 - A parameter of interest is what your data is focused on. Perhaps you want to know the average weight of a 17 year old boy, your parameter of interest is the average weight of a 17 year old boy. Parameters are about an entire population, so you must state your population.
3 - A statistic is a characteristic of a sample. Generally, a statistic is used to estimate the value of a population parameter. For instance, suppose we selected a random sample of 100 students from a school with 1000 students.
4 - A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 1,572 adults; 1,298 of them own a cell phone, hence 1298∕1572≈. 83 or about 83% own a cell phone.
Answer:
Descriptive statistics give information that describes the data in some manner. For example, suppose a pet shop sells cats, dogs, birds and fish. If 100 pets are sold, and 40 out of the 100 were dogs, then one description of the data on the pets sold would be that 40% were dogs.
This same pet shop may conduct a study on the number of fish sold each day for one month and determine that an average of 10 fish were sold each day. The average is an example of descriptive statistics.
Some other measurements in descriptive statistics answer questions such as 'How widely dispersed is this data?', 'Are there a lot of different values?' or 'Are many of the values the same?', 'What value is in the middle of this data?', 'Where does a particular data value stand with respect with the other values in the data set?'
A graphical representation of data is another method of descriptive statistics. Examples of this visual representation are histograms, bar graphs and pie graphs, to name a few. Using these methods, the data is described by compiling it into a graph, table or other visual representation.
This provides a quick method to make comparisons between different data sets and to spot the smallest and largest values and trends or changes over a period of time. If the pet shop owner wanted to know what type of pet was purchased most in the summer, a graph might be a good medium to compare the number of each type of pet sold and the months of the year.
Step-by-step explanation:
Inferential Statistics
Now, suppose you need to collect data on a very large population. For example, suppose you want to know the average height of all the men in a city with a population of so many million residents. It isn't very practical to try and get the height of each man.
This is where inferential statistics comes into play. Inferential statistics makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician