Exam 10: Estimation: Describing a Single Population

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

An interval estimate is a range of values within which the actual value of a population parameter  falls.

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both $n \hat p$ and $n \hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of:

At a given sample size and level of confidence, the smaller the population standard deviation?, the wider and thus the less precise the confidence interval estimate of ? is.

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Determine the 95% confidence interval estimate of the population mean, changing the population standard deviation to 2.

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

The width of a confidence interval increases as the level of significance increases.

How large a sample must be drawn to estimate the proportion of students who prefer statistics over mathematics, to within 0.02 with 95% confidence?

In general, decreasing the confidence level ( $1 - \alpha$ ) will narrow the interval.

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. What happens to the width of the confidence interval estimate when each of the following things happens? a. The confidence level increases. b. The confidence level decreases. c. The sample size increases. d. The sample size decreases. e. The value of the population standard deviation increases. f. The value of the population standard deviati on decreases. g. The value of the sample mean increases. h. The value of the sample mean decreases.

Which of the following is true about the t-distribution?

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

Find and interpret a 98% confidence interval for the mean number of animals visited by a veterinarian per day. A random sample of 35 veterinarians, found that they had a sample mean of 25.3 animals and a sample variance of 2.8 animals.

Suppose that a 95% confidence interval for ? is given by $\bar { X } \pm 3.25$ . This notation means that if we repeatedly draw samples of the same size from the same population, 95% of the values of $\bar { x }$ will be such that ? would lie somewhere between $\bar { X } - 3.25$ and $\bar { X } + 3.25$ .

The sample size needed to estimate a population mean to within 2 units with a 95% confidence when the population standard deviation equals 8 is:

An interval estimate is an estimate of the range for a population parameter.

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Interpret what the confidence interval estimate tells you.

A random sample of 10 university students was surveyed to determine the amount of time they spent weekly using a personal computer. The times (in hours) were: 13 14 5 6 8 10 7 12 15 3 If the times are normally distributed with a standard deviation of 5.2 hours, estimate with 90% confidence the mean weekly time spent using a personal computer for all university students.