BackTrue or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
As the sample size increases, the standard deviation of the distribution of sample means increases.
True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
As the sample size increases, the mean of the distribution of sample means increases.
In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.
Mu = 1275, sigma =6, n = 1000
In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.
Mu = 790, sigma =48, n = 250
In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.
Mu = 45, sigma =15, n = 100
In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.
Mu = 150, sigma =25, n = 49
Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.
For a random sample of n=36, find the probability of a sample mean being less than 12,750 or greater than 12,753 when mu=12750 and 1.7.
Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.
For a random sample of n=45, find the probability of a sample mean being greater than 551 when mu=550 and sigma=3.7.
Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.
For a random sample of n=64, find the probability of a sample mean being less than 24.3 when Mu=24 and sigma=1.25.
True or False: To construct a confidence interval about a population variance or standard deviation, either the population from which the sample is drawn must be normal, or the sample size must be large.
The procedure for constructing a confidence interval about a mean is ________, which means minor departures from normality do not affect the accuracy of the interval.
Critical Values Sir R. A. Fisher, a famous statistician, showed that the critical values of a chi-square distribution can be approximated by the standard normal distribution
χ²_k = [(z_k + √(2v – 1)) / 2]²
where v is the degrees of freedom and z_k is the z-score such that the area under the standard normal curve to the right of z_k is k. Use Fisher’s approximation to find χ²_0.975 and χ²_0.025 with 100 degrees of freedom. Compare the results with those found in Table VIII.
If we wish to obtain a 95% confidence interval of a parameter using the bootstrap percentile method, we determine the_______percentile and the_______ percentile of the resampled distribution.
The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = –1.56? Why?