Discuss the below:
Calculate confidence intervals when a population's standard deviation is both know and unknown, for the below:
Q1. A sample of 81 observations is taken from a normal population. The sample mean is 40, and the sample standard deviation of 5. Determine the 95 percent confidence interval for the population mean.
Q2. Merrill Lynch Securities and Health Care Retirement, Inc, are two large employers in down Toledo, OH. They are considering jointly offering child care for their employees. As a part of the feasibility study, they wish to estimate the mean weekly child-care cost of their employees. A sample of 10 employees who use child care reveals the following amounts spent last week.
$107, $92, $97, $95, $105, $101, $91, $99, $95, $104
Develop a 98 percent confidence interval for the population mean. Interpret the result.
Q3. The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes traveled.
29 38 38 33 38 21 45 34
40 37 37 42 30 29 35
Develop a 98 percent confidence interval for the population mean. Interpret the result.
Q4. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significant level?
Q5. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?