Suppose you use sampling techniques to estimate the mean of the numbers 1, 2, 3,

Question

Suppose you use sampling techniques to estimate the mean of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. To do this, you perform an experiment in which you roll a ten-sided die two times (or equivalently, roll two ten-sided dice one time) and calculate the mean of your sample. The true mean (H) of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is 5.5 ,and the true standard deviation (o) is 6.5 5.5 5.0 6.0 There are possible different samples (of size 2) you could collect in your experiment, where different, in this case, means that rolling a 1 first and then a 5 is different than rolling a 5 first and then a 1. If you collected all of these possible samples, the mean of your sampling distribution of means (H) would equal and the standard deviation of the sampling distribution of means (the standard error or ) would be The following chart shows the sampling distribution of the mean (X) for your experiment. Suppose you do this experiment once (that is, you roll the die two times). Use the chart to determine the probability that the mean of your two rolls is equal to the true mean, or P(X = ), is less than 9.5, or P(X

Explanation / Answer

Q1.
Mean = Sum of observations/ Count of observations
Mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 / 10) = 5.5
Variance
Step 1: Add them up
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Step 2: Square your answer
55*55 =3025
…and divide by the number of items. We have 10 items , 3025/10 = 302.5
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2 = 385
Step 4: Subtract the amount in Step 2 from the amount in Step 3
385 - 302.5 = 82.5
Step 5: Subtract 1 from the number of items in your data set, 10 - 1 = 9
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
82.5 / 9 = 9.1667
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
3.0277

Q2.
the total possible samples are = 10^2 = 100, there are 100 possible diffrent sample

Q3.
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 2 * 0.1
= 0.2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 2 * 0.1 * 0.9
= 0.18
III.
standard deviation = sqrt( variance ) = sqrt(0.18)
=0.424264

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