A. Is $907 a parameter or a statistic? Explain. B. For this study identify the p
ID: 3057507 • Letter: A
Question
A. Is $907 a parameter or a statistic? Explain.
B. For this study identify the population of interest, sample selected and parameter of interest.
Let µ denote the true population mean amount that was expected to be spent on Christmas gifts and let represent the true standard deviation of these amounts.
C. The sample mean is $907 while the value of the true population mean, µ, is fixed and unknown. How likely is it to obtain this particular sample mean if µ was actually $899? How likely is it to obtain this particular sample mean if µ was actually $885? What about if µ was actually $1000?
D. Assume that = $250. What does the Central Limit Theorem say about how the sample mean would vary if samples of size n = 1,028 were taken over and over? Justify.
The fígure below shows an Excel worksheet that computes normal probabilities for you. Use this example to answer the problem on the next page 1 Mean 2 St Dev 2 4 X Value S P(XK 9) 6 P(X>9 9 0.841345| NORM.DIST(B4, B1, B2, TRUE) 0.1586551-NORMDIST(B4, Bl, B2, TRUE) 8 9 10 11 12 From X Value To XValue P(XExplanation / Answer
Answer to part a)
The characteristics that define the sample data are termed as statistics
The characteristics that define the population data are termed as parameter
Hence $907 is the sample mean here, thus it is a Statistic
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Answer to part b)
The population of interest is the people who are celebrating Christmas. The parameter is average expense made on gifts of Christmas. The sample chosen will be a few people out of the population of interest who have made expenses on the Christmas gifts.
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Answer to part c)
If the sample mean is 907
We need to figure what is the possibility of getting this sample mean , based on different values of population mean.
If the population mean is : 899 , then the sample mean is pretty close to it , chances of obtaining this sample mean $907 are higher
If the population mean is: 885 , that is a value very much different from 907, hence the chances of obtaining the sample mean of $907 are a bit little lest
If the population mean is: 1000 , it is very far away from the value 907 , hence there are least chances of obtaining a mean value of 907
Thus when the mean is 899 there are more chances of getting a sample mean of 907, the chances decrease as the population mean changes to 885 , and the chances are least for the population mean 1000
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Answer to part d)
The standard deviation of the population is provided as 250
And the sample size is: 1028
Is the sample size sample is taken over and over again , as per the central limit theorem the Sample mean is not influenced by the sample size.
Sample mean will be same as the population mean irrespective of the sample size , the only condition that applies is that the sample size must be large, it does not matter what the exact size is when we deal with sample mean
When we discuss sample standard deviation, it gets influenced by the sample size. The Larger the sample smaller the standard error value is and vice-versa
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