Exam 9: Estimation and Confidence Intervals

For a given confidence level, the value of t ___________ as the sample size increases.

For a distribution of sample means with a known population standard deviation, about _____ percent of the sample means are within three standard errors of population mean.

The t distribution approaches the ____________ distribution as the sample size increases.

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence?

The z-score or z-value corresponding to a 95.34% confidence interval is ________.

In relative terms, a _______ standard deviation leads to a narrower confidence interval.

Thirty-six items are randomly selected from a population of 150 items. The sample mean is 25 and the sample standard deviation is 3. What is the adjusted standard error of the mean?

To determine the value of the standard error of the mean, the standard deviation is divided by the sample size.

When the population standard deviation is known, a __________ statistic is used to compute a confidence interval.

A local retail company wants to estimate the mean amount spent by customers. Their store's budget limits the number of surveys to 225. What is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00?

A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

When using Student's t to compute an interval estimate, ___________.

How is the t distribution similar to the standard z distribution?

When a confidence interval for a population mean is constructed from sample data, __________.

Of the following characteristics, the t distribution and z distribution are the same in all BUT one. Which one is it?

A sample of 25 is selected from a known population of 100 elements. What is the finite population correction factor?

A research firm conducted a survey to determine the mean amount people spend at a popular coffee shop during a week. They found the amounts spent per week followed a normal distribution, with a population standard deviation of $4. A sample of 49 customers revealed that the mean is $25. What is the 95% confidence interval estimate of µ?

Other things being equal, a smaller sample size would result in a wider confidence interval because the standard error of the mean is ______________.

A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________.