Answer :
To construct a confidence interval for the mean age of homeowners when they bought their first house, you should use the t method.
What is used in constructing the confidence interval
In this question, it says that the standard deviation of a small group (10. 7 years), but the standard deviation of the entire population is not given. So, If you don't know the standard deviation of the population and you have a small sample size ( 34 homeowners), one should use the t-distribution to make the confidence interval.
The t-distribution considers the extra uncertainty when trying to estimate the standard deviation of a population using a sample. On the other hand, the z-distribution is used when we know the standard deviation of the population, or when we have a big sample size and can use the Central Limit Theorem to assume that the sampling distribution is normal.
Learn more about t method
https://brainly.com/question/24277447
#SPJ4
Suppose that 34 homeowners in a city are simply randomly sampled, and were asked the age they were when they bought their first house. The mean age of the sample is 38.4 years old, and the standard deviation of the sample is 10.7 years. This quiz will walk you through the steps of constructing an 80% confidence interval for the mean age homeowners were when they bought their first home. 1. (1 point)
Which is the correct method to use for constructing the confidence interval: the z method, or the t method? How do you know?
