Question

Complete parts (a) through (e) for the population data below. 3, 6, 9 To procuppeur Turuumi. d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean. n Probability 1 3 1 2 3 3 11 (Type integers or simplified fractions.) e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5. Probability n 1 2 3 (Type integers or simplified fractions.)

Answer 1

The population mean here is computed as:
Mean = (3 + 6 + 9)/3 = 6

d) For a sample size of n = 1, we see that we get the sample mean equal to 6 only when 6 is selected. Therefore 1/3 is the required probability here for n = 1.

For a sample size of n = 2, we have here:
Sample Mean(3, 6) = (3 + 6)/2 = 4.5
Sample Mean(6, 9) = (9 + 6)/2 = 7.5
Sample Mean(3, 9) = (3 + 9)/2 = 6

Again only one of the three sample means has mean of 6. Therefore 1/3 is the required probability here.

For a sample size of n = 3, the population mean is equal to sample mean = 6. Therefore 1 is the required probability here.

n Probability 1 د | نما 1 - | تي 3 | 1 |

e) As seen in the above parts, we have:

• For n = 1, sample means are 3, 6 or 9. Therefore sampling error is 0.5 or less with probability 1/3 here that is when the sample mean is 6
• For n = 2, sample means are: 4.5, 6 or 7.5. Therefore sampling error is 0.5 or less with probability 1/3 here that is when the sample mean is 6
• For n = 3, as sampe mean = population mean. Therefore 1 is the required probability here.

Therefore again we get the same probabilities here.

n Probability 1 د | نما 1 - | تي 3 | 1 |