A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?

Question

Areli Kelly

Mathematics

18 October, 15:37

A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?

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Alvaro Mckay · Answer 1

To calculate the z-statistic, we must first calculate the standard error.

Standard error is standard deviation divided by the square root of the population. In this case, it is equal to 1.81.

The z-score is defined the distance from the sample to the population mean in units of standard error.

z = (26 - 20) / 1.81 = 3.31

at this z-score = 0.0005 which is less than 5%