BackIn Exercises 51 and 52, a population and sample size are given. (a) Find the mean and standard deviation of the population.
The goals scored in a season by the four starting defenders on a soccer team are 1, 2, 0, and 3. Use a sample size of 2.
Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.
SAT Italian Subject Test The scores on the SAT Italian Subject Test for the 2018–2020 graduating classes are normally distributed, with a mean of 628 and a standard deviation of 110. Random samples of size 25 are drawn from this population, and the mean of each sample is determined.
In Exercises 39 and 40, determine whether the finite correction factor should be used. If so, use it in your calculations when you find the probability.
Parking Infractions In a sample of 1000 fines issued by the City of Toronto for parking infractions in September of 2020, the mean fine was \$49.83 and the standard deviation was \$52.15. A random sample of size 60 is selected from this population. What is the probability that the mean fine is less than \$40?
In Exercises 51 and 52, a population and sample size are given. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population.
The goals scored in a season by the four starting defenders on a soccer team are 1, 2, 0, and 3. Use a sample size of 2.
In Exercises 53 and 54, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.
The population densities in people per square mile in the 50 U.S. states have a mean of 199.6 and a standard deviation of 265.4. Random samples of size 35 are drawn from this population, and the mean of each sample is determined.
In Exercises 53 and 54, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.
The test scores for the Law School Admission Test (LSAT) in a recent year are normally distributed, with a mean of 151.88 and a standard deviation of 9.95. Random samples of size 40 are drawn from this population, and the mean of each sample is determined.
For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning.
a. 90%
b. 95%
c. 98%
d. 99%
In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.
c = 0.80
In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.
c = 0.97
Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.
Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.
In Exercises 13–16, find the margin of error for the values of c, σ and n.
c = 0.95, σ = 5.2, n = 30
In Exercises 13–16, find the margin of error for the values of c, σ and n.
c = 0.975, σ = 4.6, n = 100
Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.
c = 0.88
In Exercises 21–24, construct the indicated confidence interval for the population mean μ.
c = 0.95, xbar = 31.39, σ = 0.80, n = 82.