 7.7.1: Applet Exercise In Example 7.1, we derived the mean and variance of...
 7.7.2: Refer to Example 7.1 and Exercise 7.1. a Use the method of Example ...
 7.7.3: Applet Exercise Refer to Exercise 7.1. Use the applet DiceSample an...
 7.7.4: Applet Exercise The population corresponding to the upper face obse...
 7.7.5: Applet Exercise What does the sampling distribution of the sample m...
 7.7.6: Applet Exercise What is the effect of the sample size on the sampli...
 7.7.7: Applet Exercise What does the sampling distribution of the sample v...
 7.7.8: Applet Exercise What is the effect of the sample size on the sampli...
 7.7.9: Refer to Example 7.2. The amount of fill dispensed by a bottling ma...
 7.7.11: A forester studying the effects of fertilization on certain pine fo...
 7.7.12: Suppose the forester in Exercise 7.11 would like the sample mean to...
 7.7.13: The Environmental Protection Agency is concerned with the problem o...
 7.7.14: If in Exercise 7.13 we want the sample mean to differ from the popu...
 7.7.15: Suppose that X1, X2,..., Xm and Y1, Y2,..., Yn are independent rand...
 7.7.16: Referring to Exercise 7.13, suppose that the effects of copper on a...
 7.7.17: Applet Exercise Refer to Example 7.4. Use the applet ChiSquare Pro...
 7.7.18: Applet Exercise Refer to Example 7.5. If 2 = 1 and n = 10, use the ...
 7.7.19: Ammeters produced by a manufacturer are marketed under the specific...
 7.7.21: Refer to Exercise 7.13. Suppose that n = 20 observations are to be ...
 7.7.22: Applet Exercise As we stated in Definition 4.10, a random variable ...
 7.7.23: Applet Exercise a Use the applet ChiSquare Probabilities and Quant...
 7.7.24: Applet Exercise Refer to Example 7.6. Suppose that T has a t distri...
 7.7.25: Applet Exercise Suppose that T is a tdistributed random variable. ...
 7.7.26: Refer to Exercise 7.11. Suppose that in the forest fertilization pr...
 7.7.27: Applet Exercise Refer to Example 7.7. If we take independent sample...
 7.7.28: Applet Exercise Suppose that Y has an F distribution with 1 = 4 num...
 7.7.29: If Y is a random variable that has an F distribution with 1 numerat...
 7.7.31: a Use Table 7, Appendix 3, to find F.01 for Fdistributed random va...
 7.7.32: Applet Exercise a Find t.05 for a tdistributed random variable wit...
 7.7.33: Use the structures of T and F given in Definitions 7.2 and 7.3, res...
 7.7.34: Suppose that W1 and W2 are independent 2distributed random variabl...
 7.7.35: Refer to Exercise 7.34. Suppose that F has an F distribution with 1...
 7.7.36: Let S2 1 denote the sample variance for a random sample of ten ln(L...
 7.7.37: Let Y1, Y2,..., Y5 be a random sample of size 5 from a normal popul...
 7.7.38: Suppose that Y1, Y2,..., Y5, Y6, Y , W, and U are as defined in Exe...
 7.7.39: Suppose that Y1, Y2,..., Y5, Y6, Y , W, and U are as defined in Exe...
 7.7.41: Applet Exercise Refer to Exercise 7.40. Use the applet SampleSize t...
 7.7.42: The fracture strength of tempered glass averages 14 (measured in th...
 7.7.43: An anthropologist wishes to estimate the average height of men for ...
 7.7.44: Suppose that the anthropologist of Exercise 7.43 wants the differen...
 7.7.45: Workers employed in a large service industry have an average wage o...
 7.7.46: The acidity of soils is measured by a quantity called the pH, which...
 7.7.47: Suppose that the scientist of Exercise 7.46 would like the sample m...
 7.7.48: An important aspect of a federal economic plan was that consumers w...
 7.7.49: The length of time required for the periodic maintenance of an auto...
 7.7.51: Refer to Exercise 7.50. If the standard deviation of shear strength...
 7.7.52: Resistors to be used in a circuit have average resistance 200 ohms ...
 7.7.53: Onehour carbon monoxide concentrations in air samples from a large...
 7.7.54: Unaltered bitumens, as commonly found in leadzinc deposits, have at...
 7.7.55: The downtime per day for a computing facility has mean 4 hours and ...
 7.7.56: Many bulk productssuch as iron ore, coal, and raw sugarare sampled ...
 7.7.57: Twentyfive heat lamps are connected in a greenhouse so that when o...
 7.7.58: Suppose that X1, X2,..., Xn and Y1, Y2,..., Yn are independent rand...
 7.7.59: An experiment is designed to test whether operator A or operator B ...
 7.7.61: Refer to Exercise 7.60. Suppose that n1 = n2 = n, and find the valu...
 7.7.62: The times that a cashier spends processing individual customers ord...
 7.7.63: Refer to Exercise 7.62. Find the number of customers n such that th...
 7.7.64: Applet Exercise Access the applet Normal Approximation to Binomial ...
 7.7.65: Applet Exercise Suppose that Y has a binomial distribution with n =...
 7.7.66: Applet Exercise Refer to Exercise 7.65. In that case, P(Y 1) = P(Y...
 7.7.67: Applet Exercise Suppose that Y has a binomial distribution with p =...
 7.7.68: Applet Exercise In 2004 Florida was hit by four major hurricanes. I...
 7.7.69: Refer to Exercise 7.68. a Based on your answer to Exercise 7.68(a),...
 7.7.71: Refer to Exercise 7.70. a For what values of n will the normal appr...
 7.7.72: A machine is shut down for repairs if a random sample of 100 items ...
 7.7.73: An airline finds that 5% of the persons who make reservations on a ...
 7.7.74: According to a survey conducted by the American Bar Association, 1 ...
 7.7.75: A pollster believes that 20% of the voters in a certain area favor ...
 7.7.76: Show that the variance of Y/n, where Y has a binomial distribution ...
 7.7.77: The manager of a supermarket wants to obtain information about the ...
 7.7.78: If the supermarket manager (Exercise 7.77) samples n = 50 customers...
 7.7.79: Suppose that a random sample of 25 items is selected from the machi...
 7.7.81: A lot acceptance sampling plan for large lots specifies that 50 ite...
 7.7.82: The quality of computer disks is measured by the number of missing ...
 7.7.83: Applet Exercise Vehicles entering an intersection from the east are...
 7.7.84: Just as the difference between two sample means is normally distrib...
 7.7.85: As a check on the relative abundance of certain species of fish in ...
 7.7.86: An auditor samples 100 of a firms travel vouchers to ascertain what...
 7.7.87: The times to process orders at the service counter of a pharmacy ar...
 7.7.88: The efficiency (in lumens per watt) of light bulbs of a certain typ...
 7.7.89: Refer to Exercise 7.88. What should be the mean efficiency per bulb...
 7.7.91: A retail dealer sells three brands of automobiles. For brand A, her...
 7.7.92: From each of two normal populations with identical means and with s...
 7.7.93: If Y has an exponential distribution with mean , show that U = 2Y/ ...
 7.7.94: A plant supervisor is interested in budgeting weekly repair costs f...
 7.7.95: A plant supervisor is interested in budgeting weekly repair costs f...
 7.7.96: Suppose that Y1, Y2,..., Y40 denote a random sample of measurements...
 7.7.97: Let X1, X2,..., Xn be independent 2distributed random variables, e...
 7.7.98: Suppose that T is defined as in Definition 7.2. a If W is fixed at ...
 7.7.99: Suppose F is defined as in Definition 7.3. a If W2 is fixed at w2, ...
 7.7.101: In the interest of pollution control, an experimenter wants to coun...
 7.7.102: Y , the number of accidents per year at a given intersection, is as...
 7.7.103: An experimenter is comparing two methods for removing bacteria colo...
 7.7.104: Let Yn be a binomial random variable with n trials and with success...
 7.7.105: If the probability that a person will suffer an adverse reaction fr...
Solutions for Chapter 7: Sampling Distributions and the Central Limit Theorem
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 7: Sampling Distributions and the Central Limit Theorem
Get Full SolutionsSince 95 problems in chapter 7: Sampling Distributions and the Central Limit Theorem have been answered, more than 129765 students have viewed full stepbystep solutions from this chapter. Chapter 7: Sampling Distributions and the Central Limit Theorem includes 95 full stepbystep solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Bimodal distribution.
A distribution with two modes

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Density function
Another name for a probability density function

Error of estimation
The difference between an estimated value and the true value.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.