Calculus and Above

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1. Strategic business planning is...

1. Strategic business planning is required for the successful transfer of control between generations in family-owned companies. However, a survey of 417 privately held family firms whose annual turnover exceeded one million dollars it was found that 87 had no strategic business plan. Assuming that simple random sampling was employed to determine the sample for the survey, estimate with 85% confidence the PROPORTION of family-owned companies operating without strategic business plans. Give the lower limit only and report your answer correct to three decimal places.

2. The R# XXXXX Centre undertook a survey to determine the average waiting time of patients in the surgery before they saw a doctor. From 18 responses, the average and standard deviation of the waiting times was found to be 9.7 and 2.6 minutes, respectively. Assuming the information was collected through a random sample and that the waiting time is approximately normally distributed, calculate a 95% confidence interval for the mean waiting time at the medical centre. State the upper bound correct to 3 dec pl.

3. GSK Pharmaceuticals wish to ensure that their Paracetamol tablets contain, on average, the amount quoted on the packet of their product - namely 500 mg. Clinical tests on a random sample of 43 tablets yielded an average of 539.89 mg of Paracetamol per tablet. It can be assumed, on the basis of previous trials, that the standard deviation of Paracetamol in each tablet is 9.6 mg. Construct a 97% confidence interval for the average amount of Paracetamol. Report only the lower limit correct to two decimal places

4. The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 15 and 18 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 27.014 kg and 0.351 kg for machine 1 and 23.935 kg and 0.38 kg for machine 2. Hence, under the usual assumptions, determine a 95% confidence interval for the difference between the average weight of the output of machine 1 and machine 2. Use machine 1 minus machine 2, stating the upper limit of the interval correct to 3 decimal places.

5. Given that sample data is presented in the file P08.10, use Kaddstat and the data to determine the 94% confidence interval for the population mean. State the lower bound and the upper bound correct to 3 decimal places.

6. People in the aerospace industry conducted a pilot study to determine the relationship between the weight and cost of a major object being sent into space. Suppose the results of the pilot study are in datafile SP13.53. Determine the number of observations needed to be 91% confident that the estimate of the average weight is within 0.25 units of the overall mean weight. Assume that the pilot study standard deviation is a good estimate of the population standard deviation and use z value from tables.

7. If you wish to estimate a population mean to within 1.75 using a 90% confidence interval and you know from prior sampling that the standard deviation is approximately equal to 7.09, use Kaddstat to determine at least how many observations you would have to include in your sample.

8. An economist with the Liquor, Hospitality and Miscellaneous Workers' Union collected data on the weekly salaries of workers in the hospitality industry in Cairns and Townsville. The union believed that the weekly salaries of employees in Cairns were higher and they were mounting a case for the equalisation of salaries between the two cities. The researcher took samples of size 24 and 21 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $574.50 and $51.96 respectively in Townsville, and $600.74 and $60.32 in Cairns. Use Cairns minus Townsville and answer correct to two decimal places.

1. Determine a point estimate for the value of the difference in average weekly salary between the two groups in dollars. 2. Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance. 3. Use Kaddstat to determine a 90% confidence interval for the difference between the average weekly salaries in Cairns and Townsville. lower limit upper limit

2. The R# XXXXX Centre undertook a survey to determine the average waiting time of patients in the surgery before they saw a doctor. From 18 responses, the average and standard deviation of the waiting times was found to be 9.7 and 2.6 minutes, respectively. Assuming the information was collected through a random sample and that the waiting time is approximately normally distributed, calculate a 95% confidence interval for the mean waiting time at the medical centre. State the upper bound correct to 3 dec pl.

3. GSK Pharmaceuticals wish to ensure that their Paracetamol tablets contain, on average, the amount quoted on the packet of their product - namely 500 mg. Clinical tests on a random sample of 43 tablets yielded an average of 539.89 mg of Paracetamol per tablet. It can be assumed, on the basis of previous trials, that the standard deviation of Paracetamol in each tablet is 9.6 mg. Construct a 97% confidence interval for the average amount of Paracetamol. Report only the lower limit correct to two decimal places

4. The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 15 and 18 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 27.014 kg and 0.351 kg for machine 1 and 23.935 kg and 0.38 kg for machine 2. Hence, under the usual assumptions, determine a 95% confidence interval for the difference between the average weight of the output of machine 1 and machine 2. Use machine 1 minus machine 2, stating the upper limit of the interval correct to 3 decimal places.

5. Given that sample data is presented in the file P08.10, use Kaddstat and the data to determine the 94% confidence interval for the population mean. State the lower bound and the upper bound correct to 3 decimal places.

6. People in the aerospace industry conducted a pilot study to determine the relationship between the weight and cost of a major object being sent into space. Suppose the results of the pilot study are in datafile SP13.53. Determine the number of observations needed to be 91% confident that the estimate of the average weight is within 0.25 units of the overall mean weight. Assume that the pilot study standard deviation is a good estimate of the population standard deviation and use z value from tables.

7. If you wish to estimate a population mean to within 1.75 using a 90% confidence interval and you know from prior sampling that the standard deviation is approximately equal to 7.09, use Kaddstat to determine at least how many observations you would have to include in your sample.

8. An economist with the Liquor, Hospitality and Miscellaneous Workers' Union collected data on the weekly salaries of workers in the hospitality industry in Cairns and Townsville. The union believed that the weekly salaries of employees in Cairns were higher and they were mounting a case for the equalisation of salaries between the two cities. The researcher took samples of size 24 and 21 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $574.50 and $51.96 respectively in Townsville, and $600.74 and $60.32 in Cairns. Use Cairns minus Townsville and answer correct to two decimal places.

1. Determine a point estimate for the value of the difference in average weekly salary between the two groups in dollars. 2. Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance. 3. Use Kaddstat to determine a 90% confidence interval for the difference between the average weekly salaries in Cairns and Townsville. lower limit upper limit

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