 7.1: Consider a population consisting of five values1, 2, 2, 4, and 8. F...
 7.2: Suppose that a sample of size n = 2 is drawn from the population of...
 7.3: Which of the following is a random variable? a. The population mean...
 7.4: Two populations are surveyed with simple random samples. A sample o...
 7.5: How would you respond to a friend who asks you, How can we say that...
 7.6: Suppose that two populations have equal population variances but ar...
 7.7: Suppose that a simple random sample is used to estimate the proport...
 7.8: A sample of size n = 100 is taken from a population that has a prop...
 7.9: In a simple random sample of 1,500 voters, 55% said they planned to...
 7.10: True or false (and state why): If a sample from a population is lar...
 7.11: Consider a population of size four, the members of which have value...
 7.12: Consider simple random sampling with replacement. a. Show that s2 =...
 7.13: Suppose that the total number of discharges, , in Example A of Sect...
 7.14: The proportion of hospitals in Example A of Section 7.2 that had fe...
 7.15: Consider estimating the mean of the population of hospital discharg...
 7.16: True or false? a. The center of a 95% confidence interval for the p...
 7.17: A 90% confidence interval for the average number of children per ho...
 7.18: From independent surveys of two populations, 90% confidence interva...
 7.19: This problem introduces the concept of a onesided confidence inter...
 7.20: In Example D of Section 7.3.3, a 95% confidence interval for was fo...
 7.21: In order to halve the width of a 95% confidence interval for a mean...
 7.22: An investigator quantifies her uncertainty about the estimate of a ...
 7.23: a. Show that the standard error of an estimated proportion is large...
 7.24: For a random sample of size n from a population of size N, consider...
 7.25: Here is an alternative proof of Lemma B in Section 7.3.1. Consider ...
 7.26: This is another proof of Lemma B in Section 7.3.1. Let Ui be a rand...
 7.27: Suppose that the population size N is not known, but it is known th...
 7.28: In surveys, it is difficult to obtain accurate answers to sensitive...
 7.29: A variation of the method described in has been proposed. Instead o...
 7.30: Compare the accuracies of the methods of 28 and 29 by comparing the...
 7.31: Referring to Example D in Section 7.3.3, how large should the sampl...
 7.32: Referring again to Example D in Section 7.3.3, suppose that a surve...
 7.33: Two populations are independently surveyed using simple random samp...
 7.34: In a survey of a very large population, the incidences of two healt...
 7.35: A simple random sample of a population of size 2000 yields the foll...
 7.36: With simple random sampling, is X2 an unbiased estimate of 2? If no...
 7.37: Two surveys were independently conducted to estimate a population m...
 7.38: Let X1, . . . , Xn be a simple random sample. Show that 1 n _n i=1 ...
 7.39: Suppose that of a population of N items, k are defective in some wa...
 7.40: This problem presents an algorithm for drawing a simple random samp...
 7.41: In accounting and auditing, the following sampling method is someti...
 7.42: Show that the population correlation coefficient is less than or eq...
 7.43: Suppose that for Example D in Section 7.3.3, the average number of ...
 7.44: Show that Var(Y R) Var(Y ) 1 + Cx Cy _ Cx Cy 2 Sketch the graph of ...
 7.45: In the population of hospitals, the correlation of the number of be...
 7.46: Use the central limit theorem to sketch the approximate sampling di...
 7.47: For the population of hospitals and a sample size of n = 64, find t...
 7.48: A simple random sample of 100 households located in a city recorded...
 7.49: In a wildlife survey, an area of desert land was divided into 1000 ...
 7.50: Hartley and Ross (1954) derived the following exact bound on the re...
 7.51: This problem introduces a technique called the jackknife, originall...
 7.52: A population consists of three strata with N1 = N2 = 1000 and N3 = ...
 7.53: The following table (Cochran 1977) shows the stratification of all ...
 7.54: a. Suppose that the cost of a survey is C = C0 + C1n, where C0 is a...
 7.55: The designer of a sample survey stratifies a population into two st...
 7.56: How might stratification be used in each of the following sampling ...
 7.57: Consider stratifying the population of into two strata: (1, 2, 2) a...
 7.58: (Computer Exercise) Construct a population consisting of the intege...
 7.59: (Computer Exercise) Continuing with 58, divide the population into ...
 7.60: A population consists of two strata, H and L, of sizes 100,000 and ...
 7.61: The value of a population mean increases linearly through time: (t)...
 7.62: In Example B of Section 7.5.2, the standard error of Xs was estimat...
 7.63: (Openended) Monte Carlo evaluation of an integral was introduced i...
 7.64: The value of an inventory is to be estimated by sampling. The items...
 7.65: The disk file cancer contains values for breast cancer mortality fr...
 7.66: A photograph of a large crowd on a beach is taken from a helicopter...
 7.67: The data set families contains information about 43,886 families li...
Solutions for Chapter 7: Survey Sampling
Full solutions for Mathematical Statistics and Data Analysis  3rd Edition
ISBN: 9788131519547
Solutions for Chapter 7: Survey Sampling
Get Full SolutionsMathematical Statistics and Data Analysis was written by and is associated to the ISBN: 9788131519547. This textbook survival guide was created for the textbook: Mathematical Statistics and Data Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Since 67 problems in chapter 7: Survey Sampling have been answered, more than 77297 students have viewed full stepbystep solutions from this chapter. Chapter 7: Survey Sampling includes 67 full stepbystep solutions.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Bivariate normal distribution
The joint distribution of two normal random variables

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

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.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Defectsperunit control chart
See U chart

Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a modelitting process and not on replication.

Estimate (or point estimate)
The numerical value of a point estimator.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.