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Question
The reason sample variance has a divisor of n - 1 rather than n is that it makes the variance an unbiased estimate of the population variance.
Answer
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Related questions
Q:
For eight randomly selected states, the following table lists the per capita beer consumption (in gallons) and the per capita wine consumption (in gallons).Beer Wine32.2 3.129.4 4.435.3 2.334.9 1.729.9 1.428.7 1.226.8 1.241.4 3.0Calculate the rank correlation coefficient when beer consumption = x, and wine consumption = y.A. rs = .506B. rs = .703C. rs = .711D. rs = .494
Q:
A readability analysis is conducted to determine how easy four different newspapers are to read for the average citizen. The sample scores are below.A B C D50 59 45 6250 60 48 6453 63 51 6858 65 54 7059 67 55 72At the = .01 level of significance, test the claim that the four newspapers have the same readability level.A. Reject the null hypothesis.B. Do not reject the null hypothesis.
Q:
A readability analysis is conducted to determine how easy four different newspapers are to read for the average citizen. The sample scores are below.A B C D50 59 45 6250 60 48 6453 63 51 6858 65 54 7059 67 55 72Calculate H.A. 20.00B. 14.95C. 11.345D. 12.06
Q:
A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly selected students were tested.Before After100 106111 11293 9592 9099 10785 100117 126110 10598 110Calculate T- and T+.A. 44, 1B. 38.5, 6.5C. 45.5, 2.5D. 32.5, 12.5
Q:
An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers.Internet Local Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 What is the test statistic T?A. 111B. 130C. 60D. 120
Q:
Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00On average, can we conclude that the machines distribute the same amount? Test at α = .05.A. Reject the null hypothesis.B. Do not reject the null hypothesis.
Q:
Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00What is the appropriate null hypothesis for the claim that they distribute the same amount of coffee?A. H0: DA DBB. H0: DA = DBC. H0: DA DBD. H0: DA DB
Q:
An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use. Currently each programming language is used by approximately 1/3 of the programmers employed by the company. The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer. It is known that all three populations have highly skewed distributions with extreme outliers. Calculate the value of Ti (rank sum) for Program B.Program A Program B Program C9 14 1210 11 167 8 76 9 108 15 13A. 23B. 48C. 49D. 57
Q:
In a Wilcoxon rank sum test, when two or more observations are equal, we assign to each tied observation a rank equal to the _________ of the consecutive ranks.
A. average
B. median
C. sum
D. difference
Q:
The __________________ is a nonparametric counterpart of a small-sample t test for comparing two independent population locations.
A. Wilcoxon rank sum test
B. Kruskal-Wallis H test
C. Wilcoxon signed ranks test
D. sign test
Q:
In a local ice skating contest, there were 2 judges and 15 contestants. Each judge was asked to rate each contestant on a 7-point scale. The most successful candidates received a rating value of 7, while the least successful candidates received a rating value of 1. It appears that the bivariate normal probability distribution assumption was severely violated. The City Council wants to know whether the judges have similar opinions in rating ice skating competitors. At a significance level of .01, the rejection point condition for the hypothesis test is
A. reject H0 if rs > .457.
B. reject H0 if rs > .623.
C. reject H0 if rs > .441.
D. reject H0 if rs > .646.
E. reject H0 if rs > .689.
Q:
A cholesterol test was given to 10 heart patients with high cholesterol levels. The same 10 heart patients are then given a new cholesterol-reducing drug for six months. Before the patients begin taking the drug, they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined. After taking the drug for six months, the same patients are given a cholesterol test again. The pharmaceutical company manufacturing the medicine wants to know if the drug is effective in reducing the cholesterol levels of the patients. The cholesterol levels before and after taking the drug are recorded for each patient. The population of cholesterol levels is not normally distributed. Which one of the following nonparametric tests is appropriate for this problem?
A. Wilcoxon signed ranks test
B. Wilcoxon rank sum test
C. sign test
D. Kruskal-Wallis test
E. Spearman's rank correlation test
Q:
A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selects 8 repair records associated with brand A and 8 repair records associated with brand B. The distribution of repair times for both brand A and brand B is highly skewed. Which one of the following nonparametric tests is appropriate for this problem?
A. Wilcoxon signed ranks test
B. Wilcoxon rank sum test
C. sign test
D. Kruskal-Wallis test
E. Spearman's rank correlation test
Q:
The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acorn showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115. Assume the population of PSI readings is highly nonnormal. The EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards. Which one of the following tests is appropriate for this problem?A. Wilcoxon signed ranks testB. Wilcoxon rank sum testC. sign testD. Kruskal-Wallis testE. Spearman's rank correlation test
Q:
Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 38, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the starting salaries have increased in the last five years. Assume that the population of starting salaries in marketing is not normally distributed. Which one of the following tests is appropriate for this problem?A. Wilcoxon signed ranks testB. Wilcoxon rank sum testC. sign testD. Kruskal-Wallis testE. Mann-Whitney test
Q:
The Wilcoxon signed ranks test is the nonparametric counterpart of the
A. large sample test about a single population mean.
B. two independent samples t test.
C. one-way ANOVA F test.
D. paired difference t test.
E. F test for equality of population variances.
Q:
An assumption of the Wilcoxon rank sum test is that the variances of the two populations are equal.
Q:
Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.
Q:
In 25 samples of 100 units each, 75 units were found to be defective. Find the appropriate UCL and LCL for the p chart.
A. 0 to .0642
B. 0 to .0828
C. 0 to .0812
D. .0129 to .0471
E. 0 to .1324
Q:
How well a process is able to meet the requirements set forth by the process design is called
A. process leeway.
B. quality of conformance.
C. quality of performance.
D. quality of design.
Q:
If the process variability steadily increases, we would observe
A. an alternating pattern of a high value followed by a low value on the R chart.
B. an upward trend on the R chart.
C. a downward trend on the R chart.
D. an increasing gradual funnel pattern on the R chart.
E. a decreasing gradual funnel pattern on the R chart.
Q:
If a company is using an chart for a given process with measurement data, it is generally not important or necessary to use an R chart or s chart.
Q:
If a process is stable and in statistical control, it is not influenced by assignable causes of variation.
Q:
Control charts are used to reduce common causes of variation.
Q:
A sequence of steadily decreasing points on a control chart is called run down.
Q:
How well the design of the product meets and exceeds the needs and expectations of the customers is called the quality of performance.
Q:
Process leeway is the distance between natural tolerance limits and control limits.
Q:
An chart is a control chart on which individual process measurements are plotted versus time.
Q:
A manufacturer of windows produces one type that has a plastic coating. The specification limits for the plastic coating are 30 and 70. From time to time the plastic coating can become uneven. Therefore, in order to keep the coating as even as possible, thickness measurements are periodically taken at four different locations on the window. 15 subgroups were observed, each consisting of four thickness measurements, with the following results: mean of the means = = 50.05, and average range = 8.85. Calculate the center line for the R chart.
A. 50.05
B. 8.85
C. 2.21
D. 0.59
Q:
A motorcycle manufacturer produces the parts for its vehicles in different locations and transports them to its plant for assembly. To keep the assembly operations running efficiently, it is vital that all parts be within specification limits. One important part used in the assembly is the engine camshaft, and one important quality characteristic is the case hardness depth. Specifications state that the hardness depth must be between 3.0 mm and 6.0 mm. To investigate the process, the quality control engineer selected 25 daily subgroups of n = 5 and measured the hardness depth. The process yielded a mean of the means = 4.50 and an average range = 1.01. Calculate the center line for the X-bar chart.
A. 1.01
B. 4.50
C. 3.49
D. 0.90