Lab Assignment 8.1
- Page ID
- 36499
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Name:__________________________________________Date:____________________Row:________
Lab Assignment 8.1
1. Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.
- 𝑥̅ =________ σ =________ n =________
- Construct a 95% confidence interval for the population mean height of male Swedes.
- State the confidence interval in words.
- Find the point estimate for mean height of male Swedes
- Calculate the error bound (E).
- Express the confidence interval in 𝑥̅ ± E form.
- Sketch the graph.
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2. Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The population distribution is assumed to be normal.
- 𝑥̅ =________ σ =________ n =________
- Construct a 90% confidence interval for the population mean time to complete the tax forms.
- State the confidence interval in words.
- Sketch the graph.
3. The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with 90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922.
- Find the point estimate for mean U.S. household income.
- Find the error bound for mean U.S. household income.
- Find the critical value, Z/2 corresponding to a 88% confidence level.
2
- The cost of homes in the area are listed below. The standard deviation for this data to the nearest hundred is σ= $100,000.
$589,000; $610,000; $765,000; $750,000; $657,000; $475,000; $599,000; $799,950; $499,000;
$629,950
- Create a 95% confidence interval for the mean cost of homes in the area.
- Interpret the confidence interval in the context of the problem.
- The average height of young adult males has a normal distribution with standard deviation of 2.5 inches. You want to estimate the mean height of students at your college or university to within one inch with 90% confidence. How many male students must you measure? Write an interpretation.
- The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed? Write an interpretation.