Question

A real estate agent wants to know how many owners of homes worth over​ $1,000,000 might be considering putting their home on the market in the next 12 months. He surveys 8585 of them and finds that 2121 of them are considering such a move. Are all the assumptions and conditions for finding the sampling distribution of the proportion​ satisfied? Explain briefly.

Answer 1

NO

Explanation:

The changeability of a sampling distribution is measured by its variance or its standard deviation. The changeability of a sampling distribution depends on three factors:

1. N: The number of observations in the population.
2. n: The number of observations in the sample.
3. The way that the random sample is chosen.

We know the following about the sampling distribution of the mean. The mean of the sampling distribution (μ_x) is equal to the mean of the population (μ). And the standard error of the sampling distribution (σ_x) is determined by the standard deviation of the population (σ), the population size (N), and the sample size (n). That is

μ_x=p

σ_x== [ σ / sqrt(n) ] * sqrt[ (N - n ) / (N - 1) ]

In the standard error formula, the factor sqrt[ (N - n ) / (N - 1) ] is called the finite population correction. When the population size is very large relative to the sample size, the finite population correction is approximately equal to one; and the standard error formula can be approximated by:

σ_x = σ / sqrt(n).