Question

A sample is chosen randomly from a population that was strongly skewed to the left. a) Describe the sampling distribution model for the sample mean if the sample size is small. b) If we make the sample larger, what happens to the sampling distribution model’s shape, center, and spread? c) As we make the sample larger, what happens to the expected distribution of the data in the sample?

Answer 1

a) If the sample size is small and the population is strongly skewed to the left, the sampling distribution model for the sample mean will also be skewed to the left. b) If we make the sample larger, the sampling distribution model's shape will approach a normal distribution. c) As we make the sample larger, the expected distribution of the data in the sample will become more representative of the population distribution.

Step-by-step explanation:

a) If the sample size is small and the population is strongly skewed to the left, the sampling distribution model for the sample mean will also be skewed to the left. The mean of the sampling distribution will be less than the population mean, and the spread of the distribution will be wider than that of the population.

b) If we make the sample larger, the sampling distribution model's shape will approach a normal distribution. The center of the distribution will still be the population mean, but the spread of the distribution, as represented by the standard deviation, will decrease.

c) As we make the sample larger, the expected distribution of the data in the sample will become more representative of the population distribution. This means that the sample will provide a more accurate estimate of the population parameters, such as the mean.

Answer 2

a. The sampling distribution for the sample mean will be skewed to the left centered at the average u, and standard deviation will be ∅
`/√(n)`

b. The sample distribution will be normal in shape and will be centered at the average u, . standard deviation will be ∅
`/√(n)`1

c. As the size of the sample increases, the sample distribution should draw near and resemble the distribution of the population

Step-by-step explanation:

A sample is chosen randomly from a population that was strongly skewed to the left. a) Describe the sampling distribution model for the sample mean if the sample size is small. b) If we make the sample larger, what happens to the sampling distribution model’s shape, center, and spread? c) As we make the sample larger, what happens to the expected distribution of the data in the sample?

The following answers will march the questions above:

a. The sampling distribution for the sample mean will be skewed to the left centered at the average u, and standard deviation will be ∅
`/√(n)`

b. The sample distribution will be normal in shape and will be centered at the average u, . standard deviation will be ∅
`/√(n)`1

c. As the size of the sample increases, the sample distribution should draw near and resemble the distribution of the population