Tutorial 4
Tutorial 4: Estimations
1. A process producing bricks is known to yield output whose weights are normally distributed with a standard deviation of 0.12lb. A random sample of 40 bricks from a day's output had a mean weight of 4.07lb.
(i) Find a 99% confidence interval for the mean weight of all bricks produced on that day.
(ii) Estimate the smallest sample size required if the error in estimating the population mean weight of all bricks is to be within 0.03lb with 95% confidence.
2. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Construct a 95% confidence interval for the population mean of cleaning times.
3. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information.
8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01
Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment.
4. A manager of a factory that manufactures a component of a particular machine wants to assess the proportion of the defective items form the production floor. He has selected a random sample of 300 items and finds that 45 of them are defective.
(i) Calculate the 95% confidence interval for the proportion of defective items.
(ii) Estimate the sample size needed by the manager if he wants to have the margin error within 2%, with 95% confidence.
5. A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are under filled , two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. Suppose that the label weight on the package
1. A process producing bricks is known to yield output whose weights are normally distributed with a standard deviation of 0.12lb. A random sample of 40 bricks from a day's output had a mean weight of 4.07lb.
(i) Find a 99% confidence interval for the mean weight of all bricks produced on that day.
(ii) Estimate the smallest sample size required if the error in estimating the population mean weight of all bricks is to be within 0.03lb with 95% confidence.
2. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Construct a 95% confidence interval for the population mean of cleaning times.
3. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information.
8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01
Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment.
4. A manager of a factory that manufactures a component of a particular machine wants to assess the proportion of the defective items form the production floor. He has selected a random sample of 300 items and finds that 45 of them are defective.
(i) Calculate the 95% confidence interval for the proportion of defective items.
(ii) Estimate the sample size needed by the manager if he wants to have the margin error within 2%, with 95% confidence.
5. A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are under filled , two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. Suppose that the label weight on the package