Suppose that for the population of all unemployed individuals in Colombia, the duration of unemployment has a standard deviation of 5 weeks. A sample of 30 unemployed Colombians is selected for a follow-up study, and it is found that the sample mean \(\overline {x}\) for the duration of unemployment is 25.7 weeks.
Calculate a 95% confidence interval for the population mean duration of unemployment in Colombia.
Suppose the standard deviation of annual precipitation in Medellín and Bogotá is 4 centimeters. A sample of 30 years of precipitation data is taken for Medellín, and a sample of 45 years of precipitation data is taken for Bogotá. The sample results show an average annual precipitation of 22 centimeters for Medellín and 42 centimeters for Bogotá.
Calculate a 95% confidence interval for the population mean of annual precipitation in Medellín.
Calculate a 95% confidence interval for the population mean of annual precipitation in Bogotá.
A human resources manager is interested in conducting a study on the time that employees dedicate to participating in meetings. It is known that meetings in the company have a standard deviation of 10 minutes. The manager takes a random sample of 50 meetings, records the duration of each, and finds that the average duration of the meetings is 73 minutes.
Calculate a 90% confidence interval for the average duration of meetings in the company.
Studies show that massage therapy has a variety of health benefits and is not too costly. A sample of 60 typical one-hour massage therapy sessions showed an average cost of $59. The population standard deviation for a one-hour session is $5.50.
Calculate an interval with an 85% confidence level for the average cost of a one-hour massage session.
Elderly individuals often face challenges in finding employment. The DANE (Colombian National Administrative Department of Statistics) reported on the number of weeks it takes for a worker aged 55 or older to find employment in Antioquia. The data on the number of weeks dedicated to job searching, contained in the “JobSearch.csv” file, are consistent with the DANE’s findings.
Provide a point estimate of the population mean regarding the number of weeks it takes for a worker aged 55 or older to find a job in Antioquia.
With 95% confidence, what is the margin of error?
What is the 95% confidence interval estimate for the mean?
Note: The population standard deviation is unknown.
Suppose you want to compare food prices in Tokyo with prices in Hong Kong. The average cost of lunch for two people in a mid-range restaurant in Tokyo is $40 (source: Numbeo.com). The “HongKongMeals.csv” file contains the costs of a sample of 42 lunches for two people in mid-range restaurants in Hong Kong.
With 95% confidence, what is the margin of error?
What is the 95% confidence interval estimate for the population mean?
How do the prices of meals for two people in mid-range restaurants in Hong Kong compare to the prices of comparable meals in restaurants in Tokyo?
Note: The population standard deviation is unknown.
Health insurance companies are beginning to offer online telemedicine services that replace the traditional in-office visit. Wellpoint provides a video service that allows subscribers to connect with a doctor online and receive prescribed treatments (Bloomberg Businessweek, March 4-9, 2014). Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The “TeleHealth.csv” file presents a sample of the savings in dollars from 20 online medical consultations.
Assuming that the population is approximately symmetrical, construct a 95% confidence interval for the average savings in an online medical consultation compared to an in-office visit.
Note: The population standard deviation is unknown.
In a study on the cost of car insurance premiums in Medellín, a random sample of 20 vehicles was taken, and the values can be found in the file “AutoInsurance.csv.”
Calculate a 90% confidence interval for the average cost of car insurance premiums in Medellín.
Note: The population standard deviation is unknown.
EAFIT University wants to conduct a study to estimate the average monthly salary of recently graduated graduates from the International Business program. From similar previous studies, it is known that the population standard deviation is $1,200,000.
What should be the sample size for the research if a 99% confidence interval with a margin of error of $500,000 is desired?
Many healthcare professionals believe that excessive consumption of red meat increases the risk of heart diseases and cancer. Suppose you wish to conduct a survey to determine the annual consumption of beef by a typical American and want to use a 3-pound margin of error for estimating the confidence interval of the mean amount of beef consumed annually by the population. Use 25 pounds as the planning value for the population standard deviation and recommend a sample size for each of the following situations.
You want a 90% confidence interval for the average amount of beef consumed.
You want a 95% confidence interval for the average amount of beef consumed.
You want a 99% confidence interval for the average amount of beef consumed.
When the desired margin of error is set, what happens to the sample size as you increase the confidence level? Would you recommend using a 99% confidence interval in this case? Discuss.
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. & Cochran, J.J., 2016. Statistics for Business & Economics, 13th ed. Cengage Learning, Boston.