15.3.9: Chapter 10 Lab

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One Population Hypothesis Testing

Year	Year of Sale
Price	Sale price in $Thousands
Bedrooms	Number of bedrooms
SqrFeet	Size of home in 100's of square feet
Pool	Does a home have a pool ? (Yes/No)
Garage	Does a home have a garage? (Yes/No)
Bath	Number of Bathrooms
Distance	Distance in miles from city center
City	City Region (Fresno, Los Angeles, Sacramento, San Francisco, San Jose)
School	School District Rating (Poor, Fair, Good , Excellent)

You want to conduct a hypothesis test about the mean home prices in California using the housing data file: housing.mpj. At the 1% significance level, design the test for the hypothesis that the mean housing price is over $850,000.
1. First create a dotplot for the price data, and paste the results here. Does the value $850,000 seem to be at the center of the data, above the center of the data, or below the center of the data?
2. State the null and alternative hypotheses in words.
3. State the null and alternative hypotheses in population parameters.
4. What model are you choosing and what assumptions are needed? Do you think the skewness and high outlier are a problem in choosing this model?
5. Conduct the test at a significance level of 1%, using MINITAB command Stat>Basic Statistics>1 Population $t$‐test. Make sure you choose options to set $H_a$. Paste the results here. All price data is in $thousands, so you would enter $850,000 as 850.
6. Do you reject or fail to reject $H_o$?
7. State your conclusion in the context of the problem.
8. Using the online or Minitab power calculator, determine the power of the test if the population mean is really $900,000. Assume the standard deviation is $450,000. (Remember the data is entered in $ thousands).
9. Using the online or Minitab power calculator, determine the sample size needed to have 95% power for the test.
You want to conduct a hypothesis test about the standard deviation of home prices in California using the housing data file: housing.mpj. At the 5% significance level, design a test to support the claim that the standard deviation housing price is not $400,000.
1. State the null and alternative hypotheses in words.
2. State the null and alternative hypotheses in population parameters.
3. What model are you choosing and what assumptions are needed?
4. Conduct the test at a significance level of 5%, using MINITAB command Stat>Basic Statistics>1 Variance. Make sure you choose options to set $H_a$. Paste the results here.
5. Do you reject or fail to reject $H_o$?
6. State your conclusion in the context of the problem.
For the housing data above, we want to support the claim that the percentage of homes in California with garages is over 60%. We are going to conduct a Hypothesis Test using a significance level of 10%.
1. State the null and alternative hypotheses in words.
2. State the null and alternative hypotheses in population parameters.
3. Create a bar chart of garages and under Chart Option, click the box to show $y$ as a percentage. Does the bar graph support the claim that more than 60% of homes have garages?
4. What model are you choosing and what assumptions are needed?
5. Using the online power calculator, determine the power of the test if the population proportion under $H_a$ is 0.65
6. Conduct the test at a significance level of 5%, using MINITAB command Stat>Basic Statistics>1 Proportion. Make sure you choose options to set $H_a$. Paste the results here.
7. Do you reject or fail to reject $H_o$?
8. State your conclusion in the context of the problem.