Exam 8: Large-Sample Estimation

A recent survey indicates that the proportion of season ticket holders for the school hockey team who renew their seats is about 0.80. Using a 95% confidence interval and a margin of error of 0.025, what is the approximate size of the sample needed to estimate the true proportion who plan to renew their seats?

Which of these statements is NOT a property of the confidence interval estimate of the population mean?

Public versus Private Childcare Expenses Narrative A social worker was interested in determining whether there is a significant difference in the average monthly cost per child for childcare outside the home between publically supported facilities and privately owned facilities. Two independent random samples were selected, yielding the following information: -A statistician knows that the population of light bulb lifetimes is normally distributed and has a standard deviation of 30 hours. A simple random sample of 36 bulbs yields a mean lifetime of 504 hours. Construct and interpret a 99% confidence interval for the mean lifetime of all such bulbs.

In order to construct a confidence interval estimate of the population proportion p, the value of p is needed.

What is the approximate z-value you would use if you wish to construct a 92% lower confidence bound for the difference between population means in the case of large samples?

A process control engineer wishes to estimate the true proportion of defective computer chips, with a margin of error of no more than 0.09 and with probability 0.90. How many observations does the engineer need to include in the sample to achieve his goal? Justify your conclusion.

A study conducted by a commuter train transportation authority involved surveying a random sample of 200 passengers. The results show that a customer had to wait, on average, 9.3 minutes, with a standard deviation of 6.2 minutes, to buy a ticket. Construct a 95% confidence interval for $\mu$ , the true mean waiting time.

A point estimate is a single value estimate of the value of a population parameter.

The confidence coefficient is the probability that a confidence interval will enclose the estimated parameter.

College Beach Volleyball Narrative A student government representative at a local university claims that 60% of the undergraduate students favour a move from court volleyball to beach volleyball. A random sample of 250 undergraduate students was selected and 140 students indicated they favoured a move to beach volleyball. -Refer to College Beach Volleyball Narrative. Based on the interval in the previous question, can the representative's claim be rejected? Justify your answer.

College Beach Volleyball Narrative A student government representative at a local university claims that 60% of the undergraduate students favour a move from court volleyball to beach volleyball. A random sample of 250 undergraduate students was selected and 140 students indicated they favoured a move to beach volleyball. -Refer to College Beach Volleyball Narrative. Find a 95% confidence interval for the true proportion of undergraduate students who favour the move to beach volleyball.

The best estimator of the difference between two population means is the difference between two sample means .

A study was conducted to compare the mean numbers of police emergency calls per eight-hour shift in two districts of Toronto. Samples of 100 eight-hour shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The sample statistics are listed below: Find a 90% confidence interval for the difference in the mean numbers of police emergency calls per shift between the two districts of the city. Interpret the interval.

Whenever a sampled population is normally distributed, or whenever the conditions of the Central Limit Theorem are fulfilled, what may be said of the sample mean ?

If a store manager is interested in estimating the mean amount spent per customer per visit at her store, the sample mean would be the approximate point estimate.

When constructing a confidence interval for a population parameter, we generally set the confidence coefficient ( ) close to 0 (usually between 0 and 0.05) because it is the probability that the interval does not include the actual value of the population parameter.

An interval estimate is an interval that provides an upper and a lower bound for a specific population parameter whose value is unknown.

If a store manager has recently stated that she estimates the mean amount spent per customer per visit to be between $38.75 and $72.23, the numbers $38.75 and $72.23 are considered point estimates for the true population mean.

What is the z-value needed to construct a 97.8% confidence interval estimate for the difference between two population proportions?

In developing an interval estimate for a population mean, a sample of 40 observations was used. The interval estimate was 17.25 2.42. If the sample size had been 160 instead of 40, what would the interval estimate have been?