Question

Suppose the average size of a new house bult in a certain county in 2014 was 2.272 square feet. A random sample of 25 mew homes built in this county was selected in 2018. The average square footage was 2,189, with a sample standard deviation of 223 square feet. Complete parts a and b a. Using a =0.02, does this sample provide enough evidence to conclude that the average house rizo of a new home in the county has changed since 2014?

Answer 1

To determine if the average house size of a new home in the county has changed since 2014, we perform a hypothesis test using a two-tailed t-test. The obtained t-value is greater than the critical t-value, leading us to reject the null hypothesis. Therefore, there is enough evidence to conclude that the average house size has changed.

Step-by-step explanation:

To determine if there is enough evidence to conclude that the average house size of a new home in the county has changed since 2014, we need to perform a hypothesis test. Let's state our hypotheses:

H0: The average house size has not changed since 2014 (μ = 2272)

Ha: The average house size has changed since 2014 (μ ≠ 2272)

We will use a two-tailed t-test with alpha = 0.02.

Next, we calculate the test statistic using the formula:

t = (sample mean - population mean) / (sample standard deviation / √n)

Substituting the given values:

t = (2189 - 2272) / (223 / √25)

Calculating the test statistic, we find t ≈ -3.76.

Finally, we compare the obtained t-value with the critical t-value. Since the obtained t-value is greater than the critical t-value (2.552 for alpha = 0.02 and degrees of freedom = 24), we reject the null hypothesis.

Therefore, there is enough evidence to conclude that the average house size of a new home in the county has changed since 2014.