1. An economist is interested in studying the incomes of consumers in a country. The population...

  

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1. An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15, 000. Construct a 99% confidence interval for the average income. 2. A machine that produces control arms for a vehicle gas pedal generates pedals that have a length with standard deviation of 0.08 cm. A sample of 30 control arms has a mean of 18.2 cm. What would be the acceptable range of lengths for a 95% confidence interval for the mean length? 3. What percentage of hospitals provide at least some charity care? The following problem is based on information taken from State Health Care Data. Based on a random sample of hospital reports, the following information was obtained: 57.1 56.2 53.0 66.1 59.0 64.7 70.1 64.7 53.5 78.2 (i) Verify that the sample mean and the sample standard deviation are respec- tively X = 62.3% and s 8.0%. (ii) Find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care. 4. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the data from the 20 students, and their mean is 135.2. Is this evidence of a significantly higher score by older students? Use a significance level of 0.01. 5. An environmentalist collects a liter of water from 45 different locations along the banks of a stream. He measures the amount of dissolved oxygen in each specimen. The mean oxygen level is 4.62 mg, with the overall standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. Conduct a hypothesis test with alpha 0.001 to determine whether the mean oxygen level is less than 5 mg. 6. A bus company advertised a mean time of 150 minutes for a trip between two cities. A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 40 trips showed a man of 153 minutes and a standard deviation S = 7.5 minutes. At the 0.05 level of significance, test the consumer group's belief. 1. An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15, 000. Construct a 99% confidence interval for the average income. 2. A machine that produces control arms for a vehicle gas pedal generates pedals that have a length with standard deviation of 0.08 cm. A sample of 30 control arms has a mean of 18.2 cm. What would be the acceptable range of lengths for a 95% confidence interval for the mean length? 3. What percentage of hospitals provide at least some charity care? The following problem is based on information taken from State Health Care Data. Based on a random sample of hospital reports, the following information was obtained: 57.1 56.2 53.0 66.1 59.0 64.7 70.1 64.7 53.5 78.2 (i) Verify that the sample mean and the sample standard deviation are respec- tively X = 62.3% and s 8.0%. (ii) Find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care. 4. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the data from the 20 students, and their mean is 135.2. Is this evidence of a significantly higher score by older students? Use a significance level of 0.01. 5. An environmentalist collects a liter of water from 45 different locations along the banks of a stream. He measures the amount of dissolved oxygen in each specimen. The mean oxygen level is 4.62 mg, with the overall standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. Conduct a hypothesis test with alpha 0.001 to determine whether the mean oxygen level is less than 5 mg. 6. A bus company advertised a mean time of 150 minutes for a trip between two cities. A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 40 trips showed a man of 153 minutes and a standard deviation S = 7.5 minutes. At the 0.05 level of significance, test the consumer group's belief.

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3 Using a calculator we find that Mean 6226 623 Stand... View the full answer