A technology start-up company has had 5 different CEOs since it was founded. The

Question

A technology start-up company has had 5 different CEOs since it was founded. The tenures of these CEOs – the number of months that they held the position – are given in the table below. These 5 CEOs are the population you are interested in.

CEO

Tenure (in months)

1

12

2

14

3

6

4

19

5

12

3. Suppose that you randomly sample 2 CEOs without replacement. In the table below, list all possible samples you could select and the value of the sample mean of tenure (x ) in each sample.

4. Under simple random sampling, what is the probability of each sample you wrote down in question 3?

5. For each CEO, calculate the probability that he/she is selected into a sample. Comment on your answer.

6.Use your answers to questions 3 and 4 to write down the probability distribution of the sample mean x (i.e. a table with possible outcomes and associated probabilities).

7. Calculate the expected value of x . How does your answer compare to the population mean of tenure?

8.Suppose that you sampled 2 CEOs with replacement instead. How many different samples are possible, and what is the probability of each sample occurring?

CEO

Tenure (in months)

1

12

2

14

3

6

4

19

5

12

Explanation / Answer

Q.3 The X bar table

4. The probability of each sample is same for each sample. As there are 10 such samples can be drawn so

Probability of getting any such sample = 1/10 = 0.1

5. As we can see that out of 10 such samples, each CEO is in 4 samples.

So, probability that any given CEO is in the any sample = 4/10 = 0.4

6. Probability distribution with associated probability

7.  expected value of x . = E(X bar) = 9 * 0.2 + 10 * 0.1 + 12 * 0.1 + 12.5 * 0.1 + 13 * 0.2 + 15.5 * 0.2 + 16.5 *0.1 = 12.6

8. If we sampled  2 CEOs with replacement instead . then there will be 52 = 25 samples

Probability of each sample occurring = 1/25 = 0.04

S.NO. Sample X bar 1 (1,2) 13 2 (1,3) 9 3 (1,4) 15.5 4 (1,5) 12 5 (2,3) 10 6 (2,4) 16.5 7 (2,5) 13 8 (3,4) 12.5 9 (3,5) 9 9 (4,5) 15.5

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