The U.S. Census Bureau reported that the mean area of U.S. homes built in 2012 was 2505 square feet. A simple random sample of 20 homes built in 2013 had a mean area of 2660 square feet with a standard deviation of 200 feet. Can you conclude that the mean area of homes built in 2013 is greater than the mean area of homes built in 2012? It has been confirmed that home sizes follow a normal distribution. Use a 1% significance level. Round to the fourth H0: μ = 2505 HA: μ > 2505 Test Statistic: P-value: Did something significant happen? Nothing Significant Happened Select the Decision Rule: Fail to Reject the Null There is not enough evidence to conclude that the mean area of homes built in 2013 is greater than the mean area of homes built in 2012.
Added by James G.
Step 1
\(H_0: \mu = 2505\) \(H_A: \mu > 2505\) Show more…
Show all steps
Close
Your feedback will help us improve your experience
James Kiss and 71 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The U.S. Census Bureau reported that the mean area of U.S. homes built in 2012 was 2505 square feet. A simple random sample of 28 homes built in 2013 had a mean area of 2660 square feet with a standard deviation of 220 feet. Can you conclude that the mean area of homes built in 2013 is greater than the mean area of homes built in 2012? It has been confirmed that home sizes follow a normal distribution. Use a 10% significance level. Round to the fourth decimal place. Ho: H1: Test Statistic: P-value: Did something significant happen? Decision Rule: Is there enough evidence to conclude?
Keondre P.
During the $2007-2008$ decline in the housing market, it appeared that the average size of a newly constructed house fell. To investigate this trend, the square footages of a random sample of houses built in 2008 were compared to houses built in $2018 . \mathrm{A}$ random sample of 45 homes built in 2008 had a sample mean of $2,462.3$ square feet and a sample standard deviation of $760.8$ square feet. A random sample of 40 homes built in 2018 had a sample mean of $2,257.0$ square feet and a sample standard deviation of $730.2$ square feet. Assume that the population variances for the square footages of houses built in these two years are equal. a. Using $\alpha=0.05$, perform a hypothesis test to determine if the average home constructed in 2010 was larger than a home built in 2018 . b. Construct a $95 \%$ confidence interval to estimate the average difference in the square footages of new homes constructed in these two years. Interpret your result. c. Determine the precise $p$ -value using Excel and interpret the results. d. What assumptions need to be made in order to perform this procedure?
Jon S.
The average size of single-family homes built in the United States is 2,390 square feet (Statistical Abstract of the United States, 2011). A random sample of 100 new homes sold in California yielded the following size information: x̄ = 2,507 square feet and s = 257 square feet. a. Assume the average size of U.S. homes is known with certainty. Do the sample data provide sufficient evidence to conclude that the mean size of California homes built exceeds the national average? Test using α = .01. b. Suppose the actual mean size of new California homes was 2,490 square feet. What is the power of the test in part a to detect this 100-square-foot difference? c. If the California mean were actually 2,440 square feet, what is the power of the test in part a to detect this 50-square-foot difference?
Adi S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD