Tests for a population mean (σ Known/ σ Unknown)
1. The amount of time required to complete a critical part of a production process on an assembly line is normally distributed. The mean is believed to be 130 seconds. To test if this belief is correct, a sample of 100 randomly selected assemblies is drawn and the processing time recorded. The sample mean is 126.8 seconds. If the process time is really normal, with a standard deviation of 15 seconds, can we conclude that the belief regarding the mean is incorrect?
2. In order to determine the number of workers required to meet demand, the productivity of newly-hired trainees is studied. It is believed that trainees can process and distribute more than 450 packages per hour within one week of hiring.
Can we conclude that this belief is correct, based on productivity observation of 50 trainees which was found to have an average of 460.38 and standard deviation 38.83?
3. A company argues that its blue-collar workers, who are paid an average of $30,000 per year, are well paid because the mean annual income of all blue-collar workers in the country is less than $30,000. That figure is disputed by the union, which does not believe that the mean blue-collar income is less than $30,000. To test the company CEO's belief, an arbitrator draws a random sample of 350 blue-collar workers from across the country and asks them to report their annual income. He found that the average income of the sample is $29120. If the arbitrator assumes that the blue-collar incomes are normally distributed with a standard deviation of $8,000, can it be inferred at the 5% significance level that the company CEO is correct?
4. A growing concern for educators is the number of teenagers who have part-time jobs while they attend high school. It is generally believed that the amount of time teenagers spend working is deducted from the amount of time devoted to school work. The maximum time recommended for a part-time job is 6 hours per week. A school guidance counsellor sets out to investigate whether the average time spent working by all 15-year old school students is greater than 6 hours per week. She takes a random sample of 200 15-year olds and asks each one how many hours per week they work in a part-time job. The data is in the file Part-time jobs.xls.
(a) Perform appropriate 6 step hypothesis testing stating all your arguments/calculations. What can you conclude about the average number of hours worked by 15-year old school students?
(b) What is the p-value for the test?
(c) Based on p-value, comment on the average number of hours worked by 15-year old school students.
Tests for a population proportion, pˆ
5. The manager of a sports store is considering trading on Public holidays. She believes that a majority of consumers would consider visiting the sports store on a Public holiday.
She takes a random sample of 50 customers and finds that 29 would visit the sports store on a Public holiday. Is there significant evidence to support the manager's claim? Test at the 5% level of significance.