348 views
2 votes
It is believed that the average annual rent for office space in florence is $17.43 per square foot. a real estate agent chooses a random sample of 15 properties, and found the average rent in the sample to be $18.72 per square foot, with standard deviation $3.64. is this sufficient evidence to conclude the average rent is significantly different from $17.43 per square foot? use a significance level of α = 0.05 to test.

User Kindzoku
by
8.4k points

1 Answer

6 votes

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.

User Sundq
by
9.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.