1. In general, a …………… is a number describing some aspect of a population. a. Sample. b. Parameter. c. Inference. d. Correction factor. 2. a. b. c. d. A sample quantity that serves to estimate an unknown parameter from a population is called: An equivalence. An estimator. An inference. An hypothesis test.

3. A sample may be drawn to: a. Save needless waste of time, money, and effort. b. Discover facts about a population. c. Make inferences about a parameter. d. All of the above. 4. The measure of central tendency which is sensitive to extreme scores on the higher or lower end of a distribution is the: a. median. b. mean. c. mode. d. all of the above e. none of the above 5. A large mass of data can best be summarized pictorially by means of: a. the range b. a histogram c. the frequency table d. the variance 6. Any characteristic of a population distribution may properly be referred to as a: a. standard deviation. b. raw score. c. standard score. d. standard error. e. parameter. 7. A distribution of 6 scores has a median of 21. If the highest score increases 3 points, the median will become ___________. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information. e. none of these 8. A population is:

a. a number or measurement collected as a result of observation b. a subset of a population c. a characteristic of a population which is measurable d. a complete set of individuals, objects, or measurements having some common observable characteristics e. none of these 9. Which of the following describes a "statistical inference"? a. A true statement about a population made by measuring some sample of that population. b. A conjecture about a population made by measuring some sample of that population. c. A true statement about a sample made by measuring some population. d. A conjecture about a sample made by measuring some population. e. A true statement about a sample made by measuring the entire population....

...1 points
Questions 5 through 8 refer to the following:
In 1985, the mean weight of players in the National Football League was 225 pounds. A random sample of 50 players taken during the 2012 season showed a mean weight of 249.7 pounds with a sample standard deviation of 35.2 pounds. The researcher is interested in finding evidence at the .05 level that the mean weight of NFL players has increased since 1985.
Which of the following pairs of hypotheses is suggested by the scenario described above?
Selected Answer: D.
H0: μ = 225 HA: μ ≠ 225
Correct Answer: C.
H0: μ ≤ 225 HA: μ > 225
Question 6
1 out of 1 points
What is the value of the test statistic? Selected Answer: B.
4.962
Correct Answer: B.
4.962
Question 7
0 out of 1 points
Which of the following is(are) the correct critical value(s)? Selected Answer: D.
-2.010, 2.010
Correct Answer: B.
1.677
Question 8
1 out of 1 points
What is the correct decision? Selected Answer: A.
Reject H0
Correct Answer: A.
Reject H0
Question 9
1 out of 1 points
Questions 9 through 12 refer to the following:
A particular automotive electrical fuse is designed to disrupt a circuit at a nominal current of 10 amps. The mean and variance of the time at 11 amps required to trigger a disruption are quality characteristics specified for the proper functioning of the fuse. A sample of...

...Final Exam Review Questions You should work each of the following on your own, then review the solutions guide. DO NOT look at the solutions guide first. 1. Explain the difference between a population and a sample. In which of these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation. 2. The following numbers represent the weights in pounds of six 7year old children in Mrs. Jones' 2nd grade class. {25, 60, 51, 47, 49, 45} Find the mean; median; mode; range; quartiles; variance; standard deviation. 3. If the variance is 846, what is the standard deviation? 4. If we have the following data 34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. 5. What type of relationship is shown by this scatter plot?
45 40 35 30 25 20 15 10 5 0 0 5 10 15 20
6. What values can r take in linear regression? Select 4 values in this interval and describe how they would be interpreted.
7. Does correlation imply causation? 8. What do we call the r value. 9. To predict the annual rice yield in pounds we use the equation ˆ y = 859 + 5.76 x1 + 3.82 x2 , where x1 represents the number of acres planted (in thousands) and where x2 represents the number of acres harvested (in thousands) and where r2 = .94. a) Predict the annual yield when 3200 acres are planted and 3000 are harvested. b)...

...the Gulf. Sample data from the Multiple Listing Service in Naples, Florida, provided recent sales data for 40 Gulf View condominiums and 18 No Gulf View condominiums. Prices are in thousands of dollars.
Those analyses are below:
Descriptive Statistics for Gulf View
Gulf View List Price | Gulf View Sales Price | Gulf View Days to Sell |
Mean | 474.0075 | Mean | 454.2225 | Mean | 106 |
Median | 437 | Median | 417.5 | Median | 96 |
Maximum | 975 | Maximum | 975 | Maximum | 282 |
Minimum | 169.9 | Minimum | 165 | Minimum | 28 |
Standard Deviation | 197.29003 | Standard Deviation | 192.5177534 | Standard Deviation | 58.2168207 |
Based on the chart, the mean was calculated by adding up the sum of the list and divide 40, which the number of the total listed prices. The mean is 474,007.5, which mean the average of the listed price. Secondly, the median was calculated by listing the number in numerical order from lowest to highest and located the number in the middle 437,000. The median represents the middle number of the listed price. After calculating the median I located the minimum and maximum based the lowest and highest data, which are 169,900 and 975,000. These represent the range of the listed price. Lastly, I used the formula to get the standard deviation of 197,290.03, which measures the variability.
To calculate the mean I added up...

...compute probabilities related to the samplemean and the sample proportion The importance of the Central Limit Theorem
7-2
Why Sample?
DCOVA
Selecting a sample is less time-consuming than selecting every item in the population (census).
An analysis of a sample is less cumbersome and more practical than an analysis of the entire population.
7-3
A Sampling Process Begins With A Sampling Frame DCOVA
The sampling frame is a listing of items that make up the population Frames are data sources such as population lists, directories, or maps Inaccurate or biased results can result if a frame excludes certain portions of the population Using different frames to generate data can lead to dissimilar conclusions
7-4
Types of SamplesSamples
DCOVA
Non-Probability Samples
Probability Samples
Judgment
Convenience
Simple Random
Stratified Cluster
Systematic
7-5
DCOVA
In a nonprobability sample, items included are chosen without regard to their probability of occurrence.
In convenience sampling, items are selected based only on the fact that they are easy, inexpensive, or convenient to sample. In a judgment sample, you get the opinions of preselected experts in the subject matter.
TYPES OF SAMPLES: NONPROBABILITY...

...Guessing the Bounce Plate Affect
Abstract
The goal behind this experiment was to estimate the distance a ball would travel after it falls a certain distance and bounces off a metal plate which has an angle of 45 degrees. To find this we had to take the basic equations for kinematics which are (1/2)at2=x and v=v0+at and combine them to make an equation that will help us solve for the distance the ball will travel after hitting the bounce plate. The equation came out to be R=g*(sqrt(2)/sqrt(g))*(sqrt(H)*sqrt(h)), as that g is acceleration of gravity, h is the height of bounce plate, and H is the height of where the ball will be dropped. After completing this experiment the result was that the standard deviation was +/- 2.3 cmfrom the average value of 26.5cm. This was used for each variable H was 20cm and h was 20cm. Also there 18 trials performed as well.
Introduction
This experiment was to use kinetics of projectile motion and free falling bodies to determine the distance a ball will travel after it hits a bounce plate. To determine this we had to use the equations x=(1/2)at2 and v=v0+at and derive an equation that will determine the distance the ball will travel based on the height of the bounce plate and the height of where the ball will be dropped above the bounce plate. The equation made was g*(sqrt(2)/sqrt(g))*(sqrt(H)*sqrt(h)). From here we can make an estimate of how far the ball will travel after it hits the bounce plate.
Procedure
Materials...

...PROBABILITY AND STATISTICS
Lab, Seminar, Lecture 4.
Behavior of the sample average
X-bar
The topic of 4th seminar&lab is the average of the
population that has a certain characteristic. This average is the population parameter of interest, denoted by the greek letter mu. We estimate this parameter with the statistic x-bar, the average in the sample.
Probability and statistics - Karol Flisikowski
X-bar Definition
1 x xi n i 1
Probability and statistics - Karol Flisikowski
n
Sampling Distribution of x-bar
How does x-bar behave? To study the behavior,
imagine taking many random samples of size n, and computing an x-bar for each of the samples. Then we plot this set of x-bars with a histogram.
Probability and statistics - Karol Flisikowski
Sampling Distribution of x-bar
Probability and statistics - Karol Flisikowski
Central Limit Theorem
The key to the behavior of x-bar is the central limit
theorem. It says: Suppose the population has mean, m, and standard deviation s. Then, if the sample size, n, is large enough, the distribution of the samplemean, x-bar will have a normal shape, the center will be the mean of the original population, m, and the standard deviation of the x-bars will be s divided by the square root of n.
Probability and statistics - Karol Flisikowski
Central...

...Decision rules, either sketch or write out.
Step 4
Conclusion
Mean of difference scores
T-statistic takes the same basic form (statistic minus expected value/SD)
Reported as t(9) = .85, n.s.
Statistical decision (don’t reject null all hypothesis are plausible; reject accept all alternative hypotheses)
Interpretation
Independent group t-tests
The logic of testing hypothesis about the means of two independent groups is the same as for previous statistical tests
Some minor calculation differences that can seem difficult at first
The test provides a more detailed discussion of the standard deviation
The equation for any test may be thought of as three parts
Sample statistic
Expected value (if H0 is true)
A measure of the variability in the sample statistic
H0 is written as the difference between two means
Two assumptions greatly simplify equations
Homogeneity of Variance: it is assumed that variance in population 1 Is equal to the variance in population 2.
IMPORTANT!!!
The assumption regards the population variances, not sample variances. It is possible that s21 is not equal to s22
Second assumption… Normality
CI for a single mean
For a one sample t-test
CI = M +/- (t-critical) (sm)
Critical value was a function of df and desired level of confidence
The logic of a CI for the difference between two...

...1
“Arithmetic vs. Geometric Means: Empirical
Evidence and Theoretical Issues”
by Jay B. Abrams, ASA, CPA, MBA
Copyright 1996
There has been a flurry of articles about the relative merits of using the arithmeticmean
(AM) versus the geometric mean (GM). The Ibbotson SBBI Yearbook took the first position
that the arithmeticmean is the correct mean to use in valuation. Allyn Joyce’s June 1995
BVR article initiated arguments for the GM as the correct mean.
The previous articles have centered around Professor Ibbotson’s famous example using a
binomial distribution with 50%-50% probabilities of a +30% and -10% return. The debate
has been very interesting, but it is off on a tangent, focused on the wrong issue.
There are theoretical and empirical reasons why the arithmeticmean is the correct one.
We will look at both in this article.
Theoretical Superiority of ArithmeticMean
Rather than argue about Ibbotson’s much debated above example, I prefer to cite and
elucidate another quote from his book:
In general, the geometric mean for any time period is less than or equal to
the arithmeticmean. The two means are equal only for a return series that
is constant (i.e., the same return in every period). For a non-constant
series,...

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