What does $\bar{X}$ represent when repeatedly sampling 35 homes?

The random variable for the mean price across repeated samples; the observed sample mean is $\bar{x}$.

What is the 90% t-interval formula for the mean price of 35 sampled homes?

$\bar{x}\pm t^*\frac{s}{\sqrt{35}}$, using 34 degrees of freedom and $t^*\approx1.691$.

How is the error bound for a one-sample t interval calculated?

$\text{EBM}=t^*\frac{s}{\sqrt{n}}$; it is the distance from the sample mean to either endpoint.

What does a 90% confidence level mean for repeated samples?

About 90% of intervals constructed by the same method would contain the fixed population mean.

How does increasing confidence affect an interval based on fixed data?

It increases the critical value and error bound, making the interval wider while keeping its center fixed.

StatisticsLesson 1 of 1 in the course Confidence Intervals

One-Sample t Confidence Intervals for a County Mean Home Price

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

Save course

Lesson progress

0 / 5

Your progress is kept in this browser only.Sign up to save it

Summary

This lesson uses a random sample of 35 recently listed homes to estimate the mean cost of homes in the school’s county. You will learn how to construct and interpret a 90% confidence interval and how changing the confidence level affects its width.

Let the sale prices of the 35 randomly selected homes be the sample. The population of interest is the home prices in the county, and the parameter we want to estimate is the population mean home price, $\mu$ .

All flashcards

What does $\bar{X}$ represent when repeatedly sampling 35 homes?: The random variable for the mean price across repeated samples; the observed sample mean is $\bar{x}$ .
What is the 90% t-interval formula for the mean price of 35 sampled homes?: $\bar{x}\pm t^*\frac{s}{\sqrt{35}}$ , using 34 degrees of freedom and $t^*\approx1.691$ .
How is the error bound for a one-sample t interval calculated?: $\text{EBM}=t^*\frac{s}{\sqrt{n}}$ ; it is the distance from the sample mean to either endpoint.
What does a 90% confidence level mean for repeated samples?: About 90% of intervals constructed by the same method would contain the fixed population mean.
How does increasing confidence affect an interval based on fixed data?: It increases the critical value and error bound, making the interval wider while keeping its center fixed.

Quiz questions

What population quantity does a confidence interval based on the 35 sampled home prices estimate?Answer: The county's mean home price.
Why is a t-distribution used for the interval when estimating the population mean?Answer: The population standard deviation is unknown, so the sample standard deviation is used.
For a two-sided 90% confidence interval, how much area lies in each tail?Answer: $0.05$
What does a 90% confidence level mean in repeated sampling?Answer: About 90% of intervals constructed by the method would contain the true population mean.
If the confidence level increases while the sample data remain fixed, what happens to the interval?Answer: It becomes wider because its critical value and error bound increase.

Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

All Statistics lessons

StatisticsConstructing and Interpreting Box Plots: Quartiles, Spread, and Whiskers5 flashcards · 5 quiz questions · 4 gamesPlay free →StatisticsP-Values, Significance Levels, and Hypothesis-Test Conclusions5 flashcards · 5 quiz questions · 4 gamesPlay free →

Summary

All flashcards

Quiz questions

More in Statistics