Assessment 7
An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the upper end point in a 99% confidence interval for the average income?
$15,364
The following confidence interval is obtained for a population proportion, p: (0.399, 0.437). Use these confidence interval limits to find the margin of error, E.
0.019
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
0.0323 < p < 0.0782
True or False: The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.
False
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A random sample of 187 full-grown lobsters had a mean weight of 19 ounces and a standard deviation of 3.3 ounces. Construct a 98% confidence interval for the population mean μ.
18 oz < μ < 20 oz
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. A study involves 607 randomly selected deaths, with 35 of them caused by accidents. Construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents.
3.56% < p < 7.97%
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A random sample of 104 light bulbs had a mean life of hours with a standard deviation of (X- Bar) Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type.
539 hr < μ < 547 hr
The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress?
830
The t distribution
All of the above
After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. True or False: Referring to Scenario 8-6, 95% of the time, the sample proportion of people that recognize the product will fall between 0.36 and 0.54.
False
The president of a university would like to estimate the proportion of the student population that owns a personal computer. In a sample of 500 students, 417 own a personal computer. True or False: Referring to Scenario 8-8, we are 99% confident that the mean numbers of student population who own a personal computer is between 0.7911 and 0.8769.
False
True or False: A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.
False
True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.
False
True or False: Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval.
False
As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, = 396 and S = 100. Which of the following assumptions is necessary in order for a confidence interval to be valid?
None of these assumptions are necessary
A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "No." True or False: Referring to Scenario 8-9, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.
True
True or False: After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54.
True
True or False: The confidence interval estimate of the population mean is constructed around the sample mean.
True
True or False: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.
True
An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?
n= 1537