Sampling Distributions This exercise is to be completed in a group. For the population: 1 3 5 7 9 Find the mean and standard deviation. U = 1+3+5+7+9 / 5 = 25/5 The Mean is = 5 n= 5 The Median is = 5 Then standard deviation is = 2.828 Round to =2.83 Now determine how many samples of size 2 can be formed from this population of size 5, disregarding order. Use the appropriate formula. n=5 x=2 = n! / x! (n-x)! = 5! / 2! (5-2)! = 10 List all the samples of size 2 that can be formed from this population. Be sure the list is consistent with the answer obtained from the formula. Otherwise, check your work. (1,3), (1,5), (1,7), (1,9), (3,5), (3,7), (3,9), (5,7), (5,9) (7,9) Calculate the mean of each of the samples of size 2. 1,3 = (1+3)/2 = 2 1,5 = (1+5)/2 = 3 1,7 = (1+7)/2 = 4 1,9 = (1+9)/2 =5 3,5 =(3+5)/2 = 4 3,7 = (3+7)/2 =5 3,9 =(3+9)/2 = 6 5,7 = (5+7)/2= 6 5,9 =(5+9)/2 = 7 7,9 = (7+9)/2 = 8 Create a probability distribution of all the sample means from the sample of size 2. (HINT: If you have a mean of 7 in the list of sample means and it occurs 3 times out of 10, then the probability is 0.3 for that mean value.) Calculate the mean and standard deviation of that probability distribution using the appropriate formulas. How do the measures of the probability distribution compare to the measures from the original population? What type of probability distribution appears to be formed? Summarize any conclusions that would be fair to draw from these results.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Sampling Distributions
This exercise is to be completed in a group.
For the population: 1 3 5 7 9
Find the mean and standard deviation.
U = 1+3+5+7+9 / 5
= 25/5
The Mean is = 5
n= 5
The
Then standard deviation is = 2.828 Round to =2.83
Now determine how many samples of size 2 can be formed from this population of size 5, disregarding order. Use the appropriate formula.
n=5 x=2
= n! / x! (n-x)!
= 5! / 2! (5-2)!
= 10
List all the samples of size 2 that can be formed from this population. Be sure the list is consistent with the answer obtained from the formula. Otherwise, check your work.
(1,3), (1,5), (1,7), (1,9), (3,5), (3,7), (3,9), (5,7), (5,9) (7,9)
Calculate the mean of each of the samples of size 2.
1,3 = (1+3)/2 = 2
1,5 = (1+5)/2 = 3
1,7 = (1+7)/2 = 4
1,9 = (1+9)/2 =5
3,5 =(3+5)/2 = 4
3,7 = (3+7)/2 =5
3,9 =(3+9)/2 = 6
5,7 = (5+7)/2= 6
5,9 =(5+9)/2 = 7
7,9 = (7+9)/2 = 8
Create a
Calculate the mean and standard deviation of that probability distribution using the appropriate formulas.
How do the measures of the probability distribution compare to the measures from the original population? What type of probability distribution appears to be formed? Summarize any conclusions that would be fair to draw from these results.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
