Historical data indicated that the time required to service the conveyor belt at Coca-Cola Amatil's Richlands operations can be modeled as a normal distribution with a standard deviation of 26 minutes. A random sample of 17 services revealed a mean service duration of 90.1 minutes. Determine a 99% confidence interval for the mean service time in minutes. State the upper bound of this interval (in minutes) correct to two decimal places.
Determine the z value used to build a 90% confidence interval estimate of the population proportion. Give the positive value answer exactly as found from tables (three decimal places).
A market research company conducted a telephone survey of 195 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.222 to 0.347 was calculated. Determine the level of confidence (answer as a percentage correct to two decimal places).
Sleep apnea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of 759 Victorian commercial truck drivers found that 83 of them suffered from sleep apnea. Use the survey results to estimate, with 90% confidence, the proportion of Victorian commercial truck drivers who suffer from this sleeping disorder. Report the upper bound of the interval only, giving your answer as a percentage to two decimal places.
A sales consultant for Herron Pharmaceuticals wished to confirm that their packet of 24 paracetamol tablets was cheaper at the retail level than their rival product. The sales consultant collected price data from two independent samples, of size 19 for Herron and 26 for the rival company. These yielded an average and variance for the retail price of Herron's product of 360 cents and 72 cents squared respectively, and 380 cents and 67 cents squared for the rival. Under the usual assumptions, determine an 80% confidence interval for the price difference (use Herron minus rival) stating only the lower limit of the interval in cents (round to the nearest whole number).
A union leader in the Maritime Workers' Union believed that workers at the Port of Brisbane were receiving a lower weekly salary than workers at Port Kembla. To determine whether this claim was valid, they took samples of size 16 and 14 in Brisbane and Port Kembla, respectively, and found that the average and standard deviation of the weekly salaries were $894.15 and $61.42 respectively in Port Kembla, and $859.17 and $66.28 in Brisbane. Use Brisbane minus Port Kembla, and answer correct to two decimal places.
1. Determine a point estimate for the difference in the average weekly salary between the two ports.
2. Calculate the standard error for the difference between sample means assuming that the workers' salaries in both locations are normally distributed and have the same population variance.
3. Use Kaddstat to determine a 99% confidence interval for the difference between the mean weekly salaries in Brisbane and Port Kembla. lower limit upper limit
The R# Medical Centre undertook a survey to determine the average waiting time of patients in the surgery before they saw a doctor. From 14 responses, the average and standard deviation of the waiting times was found to be 24.3 and 10.19 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 lower bound (in minutes) correct to 3 decimal places.
The owner of a coffee shop has found that the amount spent by customers at the shop is normally distributed with a mean of $6.80 and a standard deviation of $1.20. If a random sample of 25 customers is selected, what is the probability that the average amount spent by this sample of customers will be between $6.50 and $7.40?