Exam 8: Interval Estimation

A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.8 days. Provide a 95% confidence interval for the average number of days absent per term for all the children.

A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The standard deviation of the population is known to be $66. a.Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain. b.Find the standard error of the mean. c.Give a point estimate of the population mean. d.Construct a 80% confidence interval estimates for the mean. e. Construct a 95% confidence interval for the mean.

A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below. a.What is the point estimate for the proportion of people who liked the chocolate bar? b.Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar. c.With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 3% or less?

Exhibit 8-6 A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. -Refer to Exhibit 8-6. The value of the margin of error at 95% confidence is

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is

Two hundred students are enrolled in an Economics class. After the first examination, a random sample of 6 papers was selected. The grades were 65, 75, 89, 71, 70 and 80. a.Determine the standard error of the mean. b.What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why. c.Assume the assumption of Part b is met. Provide a 95% confidence interval for the mean grade of all the students in the class.

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

In general, higher confidence levels provide

A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below. a.Compute the mean and the standard deviation of the sample. b.Compute the margin of error at 95% confidence. c.Develop a 95% confidence interval estimate for the mean of the population. Assume the population is normally distributed.

Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?

An interval estimate is a range of values used to estimate