Final answer:
To find the sample mean and sample standard deviation for the cost per square foot of the 38 new homes, multiply the average cost per square foot by the number of homes in the sample. Then, calculate the sample standard deviation using the formula for the sum of the squared differences between each individual data point and the sample mean, divided by (n-1).
Step-by-step explanation:
To find the sample mean and sample standard deviation for the cost per square foot of the 38 new homes, we can use the given information. The average cost of building a home in the Northeast is $117.91 per square foot.
Since we have a sample of 38 new homes, we can calculate the sample mean by multiplying the average cost per square foot by the number of homes in the sample: 117.91 * 38 = $4,475.58.
Next, we can calculate the sample standard deviation using the formula:
Sample standard deviation = Square root of the sum of the squared differences between each individual data point and the sample mean, divided by (n-1) where n is the size of the sample.
In this case, we need to calculate the squared differences between each individual cost per square foot and the sample mean, sum them up, divide by (38-1), and then take the square root.
This calculation can be quite involved, so it would be best to use a calculator or spreadsheet software to aid in the computation.
The resulting sample standard deviation will give us a measure of the variation in the cost per square foot among the 38 new homes.