1. What is the definition of a “randomly chosen sample” (according to the defini
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Question
1. What is the definition of a “randomly chosen sample” (according to the definition discussed in your text), and what is the goal of randomly choosing a sample?
2. Explain the relationship between error margin and sample size (assuming the confidence level remains the same), why the concept of error margin is necessary in an inductive argument, and how error margin is applied to the target population. You may want to use an example to help explain your answer.
3. Dad is making a "Hunter's Stew". The stew includes chunks of beef, potato, carrot and barley in a thick broth full of many hearty spices. As the stew is simmering in a pot on the stove, Son walks into the kitchen and says, "Let's see if this stew tastes any good!" Son gets a big spoon and begins to dip his spoon into the top of the pot. Before Son has a chance to get the spoonful of stew, Dad yells, "Mix the stew up before you taste it!" For this passage, name the intended sample, the intended target, the property in question, and explain why Son should stir the stew before he tastes it.
4. When Haley's Comet hovered over Jerusalem in 66 CE, the historian Josephus prophesied it meant the destruction of the city. Jerusalem fell four years later during a failed uprising against Roman occupiers, thus confirming the power of the comet. Is this argument subject to any causal fallacies discussed in the PowerPoint presentation for chapter 11? Explain your answer.
Explanation / Answer
1 Ans:
Simple Random Sample' A subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.
First, the word "random" in the phrase "random sample" does not have its ordinary, everyday meaning -- that is, does not refer to the first definition you would find in a dictionary.
random chosen means choose an element randomly from a group of elements.
One common mistake that arises from applying this ordinary, everyday meaning of "random" to the phrase "random sample" is concluding that a sample is not random because it has a pattern. In fact, a random sample (using the technical meaning of the phrase) might have a pattern (or it might not). In fact, there is no way we can tell from looking at the sample whether or not it qualifies as a random sample.
This brings up the second reason why the phrase is often misunderstood: The adjective "random" refers to the method by which the sample is chosen. Thus the phrase "random sample" really means "randomly chosen sample.
2Ans:
Margin of error – the plus or minus 3 percentage points in the above example – decreases as the sample size increases, but only to a point. A very small sample, such as 50 respondents, has about a 14 percent margin of error while a sample of 1,000 has a margin of error of 3 percent. The size of the population (the group being surveyed) does not matter. (This statement assumes that the population is larger than the sample.) There are, however, diminishing returns. By doubling the sample to 2,000, the margin of error only decreases from plus or minus 3 percent to plus or minus 2 percent. Although a 95 percent level of confidence is an industry standard, a 90 percent level may suffice in some instances. A 90 percent level can be obtained with a smaller sample, which usually translates into a less expensive survey. To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000.
Determining the margin of error at various levels of confidence is easy. Although the statistical calculation is relatively simple – the most advanced math involved is square root – margin of error can most easily be determined using the chart below. A few websites also calculate the sample size needed to obtain a specific margin of error. Thus, if the researcher can only tolerate a margin of error of 3 percent, the calculator will say what the sample size should be.
Consider the below table
Survey
Sample
Size
Margin
of Error
Percent*
2,000
2
1,500
3
1,000
3
900
3
800
3
700
4
600
4
500
4
400
5
300
6
200
7
100
10
50
14
Inductive arguments are arguments that try to apply what is known about known objects or situations to unknown objects or situations.
The strength of an inductive argument depends on the similarity between sample and target, and on the size of the sample.
3Ans:
For the above passage the intended sample is tastful stew, target is tastful stew. Dad is making the stew with ingrediants of beef, potato, carrot and barley andf many spices as the stew is simmering the son walk into the kitchen and witha bog spoon to dip the stew. dad give chance to the son mix the stew and taste it.
4Ans:
haley is comet it apears in jerusalem in 66 CE the historian Joseph it is symbolic of destruction of the city after the four it fall down. It was failed to raised because the romans are occupied.
the above passage is told about the power of the appearing of comet of Haley.
To answre the 4th need the" fallacies discussed in the PowerPoint presentation for chapter 11" thi s details.
Survey
Sample
Size
Margin
of Error
Percent*
2,000
2
1,500
3
1,000
3
900
3
800
3
700
4
600
4
500
4
400
5
300
6
200
7
100
10
50
14
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