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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 xare $65,100and 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 $65,100and $1018.20respectively.

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

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

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

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

The sample size is50.

02

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

The mean of x,

μx=μ=$65,100

Standard deviation of x,

role="math" localid="1652623052549" σx=σn=720050=72007.071068=$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$65,100androle="math" localid="1652623056499" $1018.20.

03

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

The mean of x,

μx=μ=$65,100
Standard deviation of x,

σx=σn=7200100=720010=$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$65,100and$720.

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