(1) According to the Australian Department of Industry, Tourism and Resources (DITR), 8.6% of the total employment in NSW is related to manufactured exports. A sample of 200 employees in NSW is randomly selected. If X is the number of employees in the sample with jobs related to manufactured exports, then the standard deviation of X is _______________.
Answer: 3.96
(2)Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20. Determine the value of x such that only 1% of the values are greater than x. (how to find the value of x with z score)
Answer: 446.6
(3) Penny Bauer, Chief Financial Officer for Harrison Haulage, suspects irregularities in the payroll system. If 10% of the 5000 payroll vouchers issued since 1 January 2005, have irregularities, the probability that Penny’s random sample of 200 vouchers will have a sample proportion .06 and .14 is ___________.
Answer: 0.9412
(4) Catherine Cho, Director of Marketing Research, needs a sample of Darwin households to participate in the testing of a new toothpaste. If 40% of the households in Darwin prefer the new toothpaste, the probability that Catherine’s random sample of 300 households will have a sample proportion between 0.35 and 0.45 is ___________.
Answer: 0.9232
(5) James Weepu, Human Resources Manager with Auckland First Bank (AFB), is reviewing the employee training programs of AFB branches. His staff randomly selected personnel files for 100 tellers in the Southern Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is ________.
Answer: 24.02 to 25.98
(6) A random sample of 64 items is selected from a population of 400 items. The sample mean is 200. The population standard deviation is 48. From this data, a 90% confidence interval to estimate the population mean can be calculated as _______.
Answer: 190.94 to 209.06
(7) A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least_____Answer: 44
(8) Restaurateur Daniel Valentine is evaluating the feasibility of opening a restaurant in Richmond. The Chamber of Commerce estimates that ‘Richmond families, on the average, dine out at least 3 evenings per week’. Daniel plans to test this hypothesis at the 0.01 level of significance. His random sample of 81 Richmond families produced a mean of 2.7. Assuming that the population standard deviation is 0.9 evenings per week, the appropriate decision is __________.
A. do not reject the null hypothesis
B. reject the null hypothesis
C. reduce the sample size
D. increase the sample size
(9) When the rod shearing process at Newcastle Steel is ‘in control’ it produces rods with a mean length of 120 cm. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The last sample showed a mean of 120.5 cm. The population standard deviation is 1.2 cm. Using α = 0.05, the appropriate decision is _________.
A. do not reject the null hypothesis and shut down the process
B. do not reject the null hypothesis and do not shut down the process
C. reject the null hypothesis and shut down the process
D. reject the null hypothesis and do not shut down the process
(10) Auckland First Bank’s policy requires consistent,standardised training of employees at all branches. Consequently, David Marshall, Human Resources Manager, orders a survey of mean employee training time in the Southern region (population 1) and the Northern region (population 2). His staff randomly selected personnel records of 81 employees from each region, and reported the following: 1= 30 hours and 2 = 27 hours. Assume that σ1 = 6, and σ2= 6. With a two-tail test and α _= .05, the appropriate decision is ______________. xx
A. reject the null hypothesis μ 1 – μ2= 0
B. accept the alternate hypothesis μ _1 – μ2< 0
C. reject the null hypothesis μ _1 – μ2≠ _0_ _
D. do not reject the null hypothesis μ1 – μ2 > 0