MATH 221 Week 5 Homework

1. Question: From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues? 2. Question: If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error? 3. Question: If a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better? 4. Question: The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 56.96. What should be done about the production line? 5. Question: In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 31.9 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer? 6. Question: What is the 99% confidence interval for a sample of 36 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches? 7. Question: If two samples A and B had the same mean and standard deviation, but sample A had a larger sample size, which sample would have the wider 95% confidence interval? 8. Question: Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean. Assume a population standard deviation of 3.8 in a normally distributed population. 9. Question: In a sample of 14 CEOs, they spent an average of 12.9 hours each week looking into new product opportunities with a sample standard deviation of 4.9 hours. Find the 95% confidence interval. Assume the times are normally distributed. 10. Question: In a sample of 32 kids, their mean time on the internet on the phone was 29.1 hours with a population standard deviation of 6.4 hours. Which distribution would be most appropriate to use? 11. Question: Under a time crunch, you only have time to take a sample of 10 water bottles and measure their contents. The sample had a mean of 20.05 ounces with a sample standard deviation of 0.3 ounces. What would be the 90% confidence interval, when we assumed these measurements are normally distributed? 12. Question: Say that a supplier claims they are 99% confident that their products will be in the interval of 50.02 to 50.38. You take samples and find that the 99% confidence interval of what they are sending is 50.00 to 50.36. What conclusion can be made? 13. Question: In a sample of 28 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 162.5 degrees with a sample standard deviation of 16.7 degrees. What would be the 95% confidence interval for the temperature of your cup of coffee? 14. Question: In a situation where the sample size was increased from 41 to 63, what would be the impact on the confidence interval? 15. Question: You needed a supplier that could provide parts as close to 76.8 inches in length as possible. You receive four contracts, each with a promised level of accuracy in the parts supplied. Which of these four would you be most likely to accept?