Exam 8: Confidence Interval Estimation

In estimating the population mean with the population standard deviation unknown,if the sample size is 12,there will be 6 degrees of freedom.

Sampling error equals to half the width of a confidence interval.

The difference between the sample proportion and the population proportion is called the sampling error.

Instruction 8-16 The Registrar of a university would like to estimate the proportion of the student population who owns a personal computer. In a sample of 500 students, 417 own a personal computer. -Referring to Instruction 8-16,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Instruction 8-19 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed 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". -Referring to Instruction 8-19,it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who feel comfortable reporting cheating by their fellow students.

The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.

Instruction 8-7 A hotel chain wants to estimate the average number of rooms rented daily in each month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms. -Referring to Instruction 8-7,during January,a sample of 16 days has a sample mean of 48 rooms.This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms.What is the level of confidence of this interval?

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option.A preliminary sample indicates that the proportion will be around 0.25.Therefore,what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

Which of the following is NOT true about the Student's t distribution?

Instruction 8-20 A business and management magazine conducted a survey on employees cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught employees cheating on an expense report, 50% have caught employees working a second job on company time, 22% have caught employees listing a "strip bar" as a restaurant on an expense report, and 19% have caught employees giving a kickback to a customer. -Referring to Instruction 8-20,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught employees cheating on an expense report is ________.

Instruction 8-17 The principal of a high school of a small suburb wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Instruction 8-17,what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Suppose a department store wants to estimate the average age of the customers of its contemporary apparel department,correct to within 2 years,with level of confidence equal to 95%.Management believes that the standard deviation is 8 years.The sample size they should take is _________.

Suppose a 95% confidence interval for $\mu$ has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval,then the resulting interval width would ________.(Assume that the sample statistics gathered would not change very much for the new sample.)

Instruction 8-17 The principal of a high school of a small suburb wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Instruction 8-17,the principle can conclude with 95% level of confidence that no more than 5% of the students in the high school skipped more than 10 days of school last year.

Instruction 8-20 A business and management magazine conducted a survey on employees cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught employees cheating on an expense report, 50% have caught employees working a second job on company time, 22% have caught employees listing a "strip bar" as a restaurant on an expense report, and 19% have caught employees giving a kickback to a customer. -Referring to Instruction 8-20,the critical value for a 95% confidence interval estimate of the population proportion of managers who have caught employees cheating on an expense report is ________.

Instruction 8-23 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. -Referring to Instruction 8-23,the sampling error is 3%.

Instruction 8-14 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognise a new product. She samples 120 potential consumers and finds that 54 recognise this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -Referring to Instruction 8-14,this interval requires the assumption that the distribution of the number of people recognising the product has a normal distribution.

Instruction 8-19 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed 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". -Referring to Instruction 8-19,we are 99% confident that the total numbers of student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

The difference between the sample mean and the population mean is called the sampling error.

An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in an average income of $30,000.What 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?