Define sampling distribution|Statistics-Maths
1. In one sentence describe why we need to do sampling in social sciences? (0.5 Points)
2. In one sentence describe the difference between statistics and parameters? (0.5 Points)
3. What is sample? (0.5 Points)
4. If y is the variable of interest, what the following symbols indicates: (1 Point)
a. μY​(​​​​​)
b. ​(​​​​​)
c. σy ​( ​)
d. σy2​(​​​​​)
5. How we differentiate proportionate stratified sampling with non-proportionate stratified sampling? (0.5 Points)
6. Only name three probability sampling approaches? (0.75 Point)
a.
b.
c.
7. If Y is the variable of interest, then what is the statistical equation indicating the relationship between the population mean and the mean of the sampling distribution? (0.25 Point)
8. What is sampling error? (0.5 Point)
9. Define sampling distribution? (0.5 Point)
10. What two qualities are used to calculate the standard error? (0.5 Point)
a.
b.
11. What is the probability of rolling an even number with a six-sided, equally weighted dice? (0.5 Point)
a.
12. Why 2. 0, 3, 6, 9 is not a sample of the population 1, 2, 3, 4, 5, 6, 7, 8, 9, 10? (0.5 Point)
13. The Law School Admission Test (LSAT) is designed so that test scores are normally distributed. The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62. If you drew all possible random samples of size 100 from the population of LSAT test-takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. What is the value of the mean of the sampling distribution? And why? (0.5 Point)
Section B: Calculations
1. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. Calculate the number of Whites selected students for a proportionate stratified random sample of 120 students? (2 Points)
2. The Law School Admission Test (LSAT) is designed so that test scores are normally distributed. The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 5.62. Calculate the value of the standard error of the mean for the sampling distribution for 100 samples. (2 Points)
3. If the mean and standard deviation of a population are 436 and 103 respectively, what is the standard error of the mean for a sample of size 8? Calculate it. (2 Points)
4. Consider the following population of 10 students with their corresponding test scores.
Student No.
Score
Student No.
Score
1
64
6
50
2
78
7
75
3
62
8
94
4
89
9
85
5
76
10
77
Calculate the sampling error for the following random sample of five students drawn from the population: Students # 4 , 10, 7 , 1 , 6. (2 Points)
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