Question

According to the Census Bureau, the mean number of people in a typical American household in 2010 was 2.6 with a standard deviation of 1.5 - this is based on the census information. Suppose, instead the Census Bureau has estimated this mean using a random sample of 225 homes - the sample mean came out to be 2.4 and standard deviation of 1.4.

What is the mean and standard error of the sampling distribution of the sample mean for 225 homes?

A) mean = 2.6, se = 0.1.
B) mean = 2.6, se = 1.5.
C) mean = 2.6, se = 1.4 .
D) mean = 2.4, se = 1.4.

Answer 1

A) mean 2.6 and standard error = 0.1

Explanation:

Explanation:-

The mean number of people in a typical American household in 2010 was 2.6 with a standard deviation of 1.5.

A random sample of 225 homes.

Given sample size 'n' =225

mean of the Population 'μ' = 2.6

Standard deviation of the Population 'σ' = 1.5

Standard error:-

Standard error of the sampling distribution of the sample mean for 225 homes.

`S.E = (S.D)/(√(n) )`

`S.E = (1.5)/(√(225) ) = 0.1`

Final answer:-

mean =2.6 and standard error =0.1