BackDegrees of Freedom For Example 1, we used df=smaller of n1-1 and n2-1 we got df=11 and the corresponding critical value is t=-1.796 (found from Table A-4). If we calculate df using Formula 9-1, we get df=19.370 and the corresponding critical value is t=-1.727 How is using the critical value of t=-1.796 “more conservative” than using the critical value of t=-1.727
Which of the following provides information about the statistical validity of Dr. Lonsbary's study?
Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.
Designing Manholes According to the website www.torchmate.com, “manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter.” Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder widths that are normally distributed with a mean of 18.2 in. and a standard deviation of 1.0 in. (based on data from the National Health and Nutrition Examination Survey).
a. What percentage of men will fit into the manhole?
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.
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?
Bachelor’s Degree in Four Years In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor’s degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.1 margin of error, and use a confidence level of 95%.
b. Assume that prior studies have shown that about 40% of full-time students earn bachelor’s degrees in four years or less.
Bachelor’s Degree in Four Years In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor’s degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.1 margin of error, and use a confidence level of 95%.
a. Assume that nothing is known about the percentage to be estimated.
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.
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.
Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.
Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B
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
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.
A sampling distribution is normal only when the population is normal.
FINDING SAMPLE SIZE Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation σ, the following formula can also be used
where corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of σ, use zα/2=1.96 and d=0.15 to get a sample size of n=86. Find the sample size required to estimate the standard deviation of IQ scores of data scientists, assuming that we want 98% confidence that s is within 5% of σ.
Alcohol in Children’s Movies Listed below is a simple random sample of times (seconds) that animated children’s movies showed the use of alcohol (based on Data Set 20 “Alcohol and Tobacco in Movies” in Appendix B).
a. Are the requirements for constructing a 95% confidence interval estimate of the population mean satisfied? If so, construct that confidence interval.
Determining Sample Size. Assume that each sample is a simple random sample obtained from a normally distributed population.
You want to estimate for the population of diastolic blood pressures of air traffic controllers in the United States. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of σ. Is this sample size practical?