Assignment -
You must use the textbook Table A.5 (to find Z values and probabilities) and Table A.7 (to find t values) to manually calculate the answers for this quiz unless explicitly stated otherwise. Tables A.5 and A.7 are also available on Blackboard under the Learning Resources. Note that if a Z value is calculated and then used to find a probability, the Z value must be rounded to 2 decimal places first to use Table A.5. Only by using Table A.5 in this way will the correct probability be found to answer these quiz questions. For example, if your Z value is 2.7890, you must look up the Z value of 2.79 in Table A.5.
For the purposes of this quiz, please ensure you ONLY use Kaddstat to calculate your answers where specifically asked to do so in the questions. Otherwise, please ensure you calculate your answers manually using the Tables and processes outlined above.
QUESTION 1 - Courier Express wished to determine the average weight of parcels carried by its Brisbane operations. On the basis of historical data, the company was aware that the weight of parcels could be approximated by a normal distribution with a variance of 0.319 kilograms squared. Last month, it weighed a random sample of 16 parcels and found the average weight was 2.171 kg. Determine a 98% confidence interval for the average weight of parcels carried by Courier Express. State the lower limit of the interval (in kg), giving your answer to three decimal places.
QUESTION 2 - In order to determine the average weight of carry-on luggage by passengers on a particular airplane, a sample of 22 pieces of carry-on luggage was weighed. The average weight was 9 kg. It is known that the weight of carry-on luggage is normally distributed and that historical data has shown the standard deviation is 3.45 kg. Determine the critical value for the test statistic (z or t) needed to build an 80% confidence interval for the mean. State the positive value exactly as found from the tables (2 decimal places).
QUESTION 3 - An interval estimate for the average distance car tyres lasted during their "lifetime" was reported to be 34121 km to 38455 km. This interval estimate was based on a sample of 66 tyres. The variance of the lifetime was determined from previous studies to be 51124695 km squared. What level of confidence can be attributed to this interval estimate? State your answer as a percentage, correct to the nearest whole number.
QUESTION 4 - Sleep apnoea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of 480 Victorian commercial truck drivers found that 84 of them suffered from sleep apnoea. Use the survey results to estimate, with 93% 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.
QUESTION 5 - 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 22 for Herron and 28 for the rival company. These yielded an average and variance for the retail price of Herron's product of 376 cents and 89 cents squared respectively, and 397 cents and 51 cents squared for the rival. Under the usual assumptions, determine a 90% confidence interval for the price difference (use Herron minus rival) stating only the upper limit of the interval in cents (round to the nearest whole number).
QUESTION 6 - 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.
1. Determine a point estimate for the value of the difference in average weekly salary between the two groups (in dollars to 2 decimal places).
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 (in dollars to 2 decimal places).
3. Use Kaddstat to determine a 90% confidence interval for the difference between the average weekly salaries in Cairns and Townsville.
QUESTION 7 - In order to determine the average weight of large post-it parcels at a post office, a sample of 31 parcels was weighed. The average weight was found to be 8.5 kg with a standard deviation of 6.4 kg. Determine a 90% confidence interval for the mean. State the lower limit only (in kg) correct to two decimal places.
Attachment:- Assignment Files.rar