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1. All possible samples of size n are selected from a population and the mean of

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Question

1. All possible samples of size n are selected from a population and the mean of each sample is determined. what is teh mean of the sample means? a) exact; b) larger than the population mean; c) smaller than the population mean; d) cannot be estimated in advance or none of them?

2. A 95% confidence interval infers that a population mean: within +_ 1.96 standard deviations or standard errors of the sample mean? or ?

3. what is the difference between a sample mean and the population mean is: a-standard error of mean, sampling error, interval estimate, point of estimate or none?

4. Central Limit Theorem, sampling distribution of sample means is a normal distribution: a-population with normal distrib., true for small sample size; b=not normal and size greater than 30; c- pop not normal and size less than 30; d-pop is normal distribute for less than 30 size; e=pop is normal distirubtion, this is true for any size sample or e=answer b and d are correct?

Explanation / Answer

Rolling a single die

1) probability of rolling divisors of 6 :

Since its a single die, the possible outcomes are 1,2,3,4,5,6. All have equal probability(1/6) since its a fair die

Out of these divisors of 6 are 1,2,3,6. So P(divisors of 6) = 1/6*1/6*1/6*1/6 = 1/1296 = 0.0008

2) probability of rolling a multiple of 1: Since all(1,2,3,4,5,6) are multiples of 6 = 1/6*1/6*1/6*1/6*1/6*1/6= 1/46656 = 0.00002

3) probability of rolling an even number : There are 3 even numbers between 1-6 i.e. 2,4,6

Hence probability of rolling an even number = 1/6*1/6*1/6 = 1/216 =0.0046

4) List of all possible outcomes of rolling a single die ={1,2,3,4,5,6}

5) probability of rolling factors of 3 : Factors of 3 are 1,3

Hence probability of rolling factors of 3 = 1/6*1/6 = 1/36 = 0.0278

6) probability of rolling a 3 or smaller : 3 or smaller are 1,2,3. Hence the probability = 1/6*1/6*1/6 = 1/216 = 0.0046

7) probability of rolling a prime number: Prime numbers between 1-6 are 2,3,5 hence probability = 1/6*1/6*1/6=1/216=0.0046

8) probability of rolling factors of 4 : Factors of 4 are 1,2,4 hence the probability = 1/6*1/6*1/6 = 1/216 =0.0046

9) probability of rolling divisors of 30 : Divisors of 30 are 1,2,3,5,6 = 1/6*1/6*1/6*1/6*1/6 = 1/7776 = 0.0001

10) probability of rolling factors of 24: Factors of 24 are 1,2,3,4,6 = 1/6*1/6*1/6*1/6*1/6=1/7776=0.0001