Question

Suppose that documentation lists the average sales price of a single-family home in the metropolitan Dallas/Ft. Worth/Irving, Texas, area as $213,200. The average home price in Orlando, Florida, is listed as $198,000. The mean of a random sample of 43 homes in the Texas metroplex was $217,800 with a population standard deviation of $30,300. In the Orlando, Florida, area a sample of 35 homes had a mean price of $204,700 with a population standard deviation of $33,800. At the 0.05 level of significance, can it be concluded that the mean price in Dallas exceeds the mean price in Orlando

Answer 1

"0.0373" seems to be the appropriate solution.

Explanation:

The given values are:

n₁ = 43

n₂ = 35

`\bar{x_1}=217800`

`\bar{x_2}=204700`

`\sigma_1=30300`

`\sigma_2=33800`

Now,

The test statistic will be:

⇒
`Z=\frac{\bar{x_1}-\bar{x_2}}\sqrt{(\sigma_1^2)/(n_1) +(\sigma_2^2)/(n_2) }`

On substituting the given values in the above formula, we get

⇒
`=\frac{217800-204400}{\sqrt{((30300)^2)/(43) +((33800)^2)/(35) } }`

⇒
`=\frac{217800-204400}{\sqrt{(918090000)/(43) +(1142440000)/(35) } }`

⇒
`=(13400)/(7347.93)`

⇒
`=1.7828`

then,

P-value will be:

=
`P(Z>1.7828)`

=
`0.0373`