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

Answer:

"0.0373" seems to be the appropriate solution.

Step-by-step 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:

⇒  $Z=\frac{\bar{x_1}-\bar{x_2}}\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }$

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

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

⇒      $=\frac{217800-204400}{\sqrt{\frac{918090000}{43} +\frac{1142440000}{35} } }$

⇒      $=\frac{13400}{7347.93}$

⇒      $=1.7828$

then,

P-value will be:

=  $P(Z>1.7828)$

=  $0.0373$