Q. 7.49 According to the U.S. Census Bur... [FREE SOLUTION]

Chapter 7: Q. 7.49 (page 301)

According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is $$65, 100$ . Assume a standard deviation of $$ 7200$ . Let x denoted the mean price of a sample of new mobile homes.
Part (a): For samples of size $50$ , find the mean and standard deviation of $x$ . Interpret your results in words.
Part (b): Repeat part (a) with $n = 100$ .

Short Answer

Expert verified

Part (a): The mean and standard deviation of $x$ are $$ 65, 100$ and role="math" localid="1652623040410" $$ 1018.20$ .

On interpreting, for samples of 50 new mobile homes, the mean and standard deviation of all possible sample mean prices are $$ 65, 100$ and $$ 1018.20$ respectively.

Part (b): The mean and standard deviation of $x$ are $$ 65, 100$ and $$ 720$ .

On interpreting, for samples of50 new mobile homes, the mean and standard deviation of all possible sample mean prices are $$ 65, 100$ and $$ 720$ .

Step by step solution

Part (a) Step 1. Given information.

Consider the given question,

The mean price of new mobile homes is $$ 65, 100$ and standard deviation is $$ 7200$ .

The sample size is50.

Part (a) Step 2. Find the mean and standard deviation when n=50.

The mean of $x$ ,

$渭_{x} = 渭 = $ 65, 100$

Standard deviation of $x$ ,

role="math" localid="1652623052549" $蟽_{x} = \frac{蟽}{\sqrt{n}} = \frac{7200}{\sqrt{50}} = \frac{7200}{7.071068} = $ 1018.20$

On interpreting, we can say that for samples of 50 new mobile homes, the mean and standard deviation of all possible sample mean prices are $$ 65, 100$ androle="math" localid="1652623056499" $$ 1018.20$ .

Part (b) Step 1. Find the mean and standard deviation when n=100.

The mean of $x$ ,

$渭_{x} = 渭 = $ 65, 100$
Standard deviation of $x$ ,

$蟽_{x} = \frac{蟽}{\sqrt{n}} = \frac{7200}{\sqrt{100}} = \frac{7200}{10} = $ 720$

On interpreting, we can say that for samples of 100 new mobile homes, the mean and standard deviation of all possible sample mean prices are $$ 65, 100$ and $$ 720$ .