Final answer:
To determine if the average rent is significantly different from $17.43, a t-test is used comparing the sample statistics against the hypothesized mean using a significance level of 0.05. The calculated t-statistic is compared with the critical value from the t-distribution table to decide if the null hypothesis can be rejected.
Step-by-step explanation:
The question you've asked is rooted in the field of statistics, and it involves conducting a hypothesis test to determine whether there's enough evidence to conclude that the average annual rent for office space in Florence is significantly different from $17.43 per square foot. Given a sample mean rent of $18.72 per square foot, a standard deviation of $3.64, and a sample size of 15 properties, we can set up a t-test to compare against our null hypothesis, which states that the average rent is $17.43 (the hypothesized mean).
To compute the t-statistic, we use the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation/√n)
Plugging in our values, we get:
t = ($18.72 - $17.43) / ($3.64/√15)
After calculating the t-statistic, we must compare it to the critical t-value for a two-tailed test at the significance level of α = 0.05, with 14 degrees of freedom (n-1 for our sample size of 15). If the absolute value of our t-statistic is greater than the critical t-value from the t-distribution table, we reject the null hypothesis, indicating that there's sufficient evidence that the average rent is significantly different from $17.43 per square foot.
If, however, the absolute value of our t-statistic is less than the critical t-value, we fail to reject the null hypothesis, meaning there is not sufficient evidence to claim a significant difference in average rent.