According to the most recent census, the average total yearly expenses of households in Wake County is $38,500. It is also known

Question

3 years ago

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According to the most recent census, the average total yearly expenses of households in Wake County is $38,500. It is also known

that the distribution of household expenses in Wake County is strongly skewed to the right with a standard deviation of $10,500. A researcher is going to randomly select a sample of 5 households from Wake County. Which of the following is true? Select all that apply.
Select one or more:

a. The sampling distribution of the sample mean will have a smaller standard deviation than the population.

b. The sampling distribution of the sample mean will have a different standard deviation than the population.

c. The sampling distribution of the sample mean will be skewed right.

d. The sampling distribution of the sample mean will have a larger standard deviation than the population.

e. We cannot tell what the shape of the sampling distribution of the sample mean will look like.

f. The shape of the sampling distribution of the sample mean will be approximately symmetric.

Mathematics

1 answer:

Alekssandra [29.7K] · Answer 1 · 2022-08-23T17:50:19+03:00

Answer:

a. The sampling distribution of the sample mean will have a smaller standard deviation than the population.

c. The sampling distribution of the sample mean will be skewed right.

Step-by-step explanation:

The mean refers to the average of a set of data which is the summation of all numbers in the data set divided by the number of values in the set.

Standard deviation is a measure that shows the extent to which each numbers in the data set is different form the value of the mean of a set of data.

Skewness is the asymmetry in or the degree of variation of a specific distribution from a normal distribution of a set of data. It is usually shown by using a symmetrical bell curve, and the curve is considered to be skewed when it is shifted to the right or left.

Since a sample of 5 household will result in a mean and standard deviation of expenses which are less than $38,500 and $10,500 respectively for the population, the sampling distribution of the sample mean will have a smaller standard deviation than the population, and the sampling distribution of the sample mean will be skewed right.