Exam 8: Estimation and Confidence Intervals

(i. The interval estimate states the range within which a population parameter probably lies. (ii) The confidence interval is the interval within which a population parameter is expected to lie. (iii) For a sampling distribution of the means, 95% percent of the means would be between $\pm$ 1.96 standard deviations.

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation is known to be $2,500. Interpret the results of the 95% confidence interval.

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $55,000. The population standard deviation is known to be $2,500. What is the 90% confidence interval for the mean salary of all graduates from the English Department?

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results: Determine a 98% confidence interval for the term test results.

The distribution of Student's t is

Student's t is used when

i. The t distribution is positively skewed. ii. All t distributions have the same mean of zero and a standard deviation of 1. iii. The t distribution is more spread out and flatter at the center than is the standard normal distribution. However, as the sample size increases, the t distribution curve approaches the standard normal distribution.

i. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution. ii. The t distribution approaches the Z distribution as the sample size increases. iii. As the sample size increases, the computed value of t decreases.

Which of the following is NOT necessary to determine how large a sample to select from a population?

Dottie Kleman is the "Cookie Lady." She bakes and sells cookies at 50 different locations. Ms. Kleman is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week pay period. The sample mean is calculated to be 1.8 and sample standard deviation is 1.1353. Develop a 95% confidence interval for the population mean. Assume that the population distribution is normal. Is it reasonable to conclude that the typical worker misses 2 days during a pay period?

A sample standard deviation is the best point estimate of the

i. One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99, but it may be any degree of confidence you specify. ii. One factor in determining the size of a sample is the maximum allowable error that you must decide on. It is the maximum error you will tolerate at a specified level of confidence. iii. The variation in the population as measured by the standard deviation has little or no effect in determining the size of a sample selected from the population.

Which statement(s) is/are correct about the t distribution?

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 95% confidence interval for the mean annual consumption of sugar.

A survey of 144 retail stores revealed that the average price of a DVD was $375 with a standard error of $20. What is the 95% confidence interval to estimate the true cost of the DVD?

If 2,000 card-carrying members of a political party were randomly sampled, and 1,600 said they wanted a change in leadership, what is the 95% confidence interval for the true population percentage for all of the card-carrying members of the party who wanted a change in leadership?

A student wanted to quickly construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 60 messages that were not business related. The 90% confidence interval for the population proportion is:

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results: If 90% and 95% confidence intervals were developed to estimate the true term test mean, what similarities would exist?

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results: Determine a 95% confidence interval for the term test results.