stats exam 3 (2)
The power of a test is
(1-β)
A probability distribution
A mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance and their corresponding probabilities
A group of 100 students were surveyed about their interest in a new Economics major. Interest was measured in terms of high, medium, or low.What is the best way to illustrate the relative frequency of student interest?
A pie chart
(0.85, 5.15)
A random sample of four observations was taken from a normal population. The results are: 1,2,4, and 5. Find: the 90% confidence interval for mue is:
(0.09,5.91)
A random sample of four observations was taken from a normal population. The results are: 1,2,4, and 5. Find: the 95% confidence interval for mue is:
3
A random sample of four observations was taken from a normal population. The results are: 1,2,4, and 5. Find: the sample mean (xbar) of the data is:
1.83
A random sample of four observations was taken from a normal population. The results are: 1,2,4, and 5. Find: the sample standard deviation (s) of the data is:
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is
0.95
The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. What is the probability that a bag of corn chips weighs between 20.75 and 23.25 ounces?
0.9876
The IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a class with 9 students, what is the probability that the class' average IQ score is between 85 and 115?
0.9974
In a binomial experiment, what does the probability of a failure equal?
1 (probability of success)
An experiment relates to outcome, as the role of a die relates to any one value between _____ and _____
1 and 6
For the most recent 7 years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?
8,327
15 accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam?
89.84
A 95% confidence interval for mu can be interpreted to mean that if we take 100 samples of the same size and construct 100 such confidence intervals for mu then
95 of the intervals are expected to include u
For a sampling distribution of the means, what % of the means would be between +- 2.576 standard deviations?
99%
A light bulb has an average service life of 750 hours, with a standard deviation of 50. If the service life of the light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 and 900 hours?
99.7%
The sign in the alternative hypothesis in a left-tailed test is always
<
The sign in the alternative hypothesis in a right-tailed test is always
>
When referring to the normal probability distribution, there is not just one; there is
A "family" of distributions
low, low, high, low
A good test is one with a ____ (low/high) probability of committing type I error (i.e., ____ α) and a ____ power (i.e., ____ β)
Type I Error
A is....
The result of a particular experiment is called a(n)
Outcome
For which of the following values of P is the value of P(1 - P) maximized? a. P = 0.99 b. P = 0.90 c. P = 0.01 d. P = 0.50
P = 0.50
The joint probability of two events, A and B, that are not dependent is computed as
P(A and B) = P(A) P(B|A)
A - chart is useful for displaying the relative frequency distribution for a nominal variable
Pie or Bar
A sample mean is a ___ of the population mean
Point estimate
A point estimate is a single value used to estimate a
Population parameter
An interval estimate is a range of values used to estimate
Population parameter
statistical power, 0, 1, β
Probability of rejecting H0 when H0 is false is ALSO KNOWN AS ____ ____. Ranges from ____ to ____. Equivalent to 1 - __.
In a bar chart, the x-axis is labeled with the values of a
Qualitative variable
The difference between the largest and smallest values in a set of data
Range
What level of measurement is the prime rate of interest
Ratio
Which level of measurement is income?
Ratio
The shape of any uniform probability distribution is
Rectangular
A pie chart shows the
Relative frequencies of a qualitative variable
Data measured on a nominal scale can only be classified into
Categories
A value that is typical or representative of the data is referred to as a measure of
Central location
This approach to probability assumes that the events are equally likely
Classical
The relationship between a parameter and its corresponding statistic can be described as which of the following?
D. All of the above
When an experiment is conducted "without replacement"
Events are dependent
(T/F) The means (x-bar s) of 98% of samples will always be within the confidence interval [x-bar-2.33(s/√N)]<u<[x-bar + 2.33(s/√N)]
False
The formula for the standard error of the proportion used in hypothesis testing is the same as that used in interval estimation
False
The sample mean is an inconsistent estimator of the population mean.
False
What type of distribution groups data into classes showing the number of observations in each class
Frequency distribution
30
General statistical practice is to assume that, for most applications, the sampling distribution of x ̄can be approximated by a normal distribution whenever the sample is size ____or more.
The measure of central location used to determine an average annual percent increase is
Geometric mean
(8.355, 11.645)
Given that xbar=10, variance=10, and n=100, construct the following confidence intervals: the 90% confidence interval for mue is:
(8.04, 11.96)
Given that xbar=10, variance=10, and n=100, construct the following confidence intervals: the 95% confidence interval for mue is:
(7.674, 12.326)
Given that xbar=10, variance=10, and n=100, construct the following confidence intervals: the 98% confidence interval for mue is:
(7.424, 12.576)
Given that xbar=10, variance=10, and n=100, construct the following confidence intervals: the 99% confidence interval for mue is:
(23.659, 26.341)
Given xbar =25, s=4 and n=16, construct the following confidence intervals: the 80% confidence interval is:
(23.247, 26.753)
Given xbar =25, s=4 and n=16, construct the following confidence intervals: the 90% confidence interval is:
(22.053, 27.947)
Given xbar =25, s=4 and n=16, construct the following confidence intervals: the 99% confidence interval is:
decreases
Standard Deviation (SD) ____ (increases/decreases) power.
decreases
Standard Error (SE) ____ (increases/decreases) power (SE is SD/√N)
The monthly Consumer Price Index is called
Statistic
The size of the sampling error is
Inversely related to the sample size (the larger the sample size, the smaller the sampling error)
The major advantage of ordinal data over nominal data is that it allows for
Order or ranking
Consumers rated a new DVD played as outstanding, very good, fair or poor. What level of measurement is this?
Ordinal
Respondents were asked, "Do you now earn more than or less than you did five years ago?" What is this level of measurement?
Ordinal
statistically significant
if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject the null hypothesis
sampling error
in the case of a random sample, the difference between the value of a sample statistic and its corresponding population parameter is
narrower
in the construction of a confidence interval for a population mean, if all other terms remain constant, an increase in the sample size will produce an interval which is:
wider
in the construction of a confidence interval for a population mean, if all other terms remain constant, an increase in the standard deviation will produce an interval which is
Type I Error
incorrect rejection of a true null hypothesis
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
interval estimate
critical region
is composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region the null hypothesis is rejected
sampling distribution
just like other random variables, x ̄has a mean or expected value, a standard deviation, and a probability distribution. Because the various possible values of x ̄are the result of different simple random samples, the probability distribution of x ̄is called the _______________ _______________ of x ̄.
frame
list of elements that the sample will be selected from
Nonsampling errors are the errors
made while collecting, recording, and tabulating data
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
margin of error
As n increases, the sample means will become ______ around the population mean.
more clustered
The further away the mean of our sample is from the hypothesized population mean, the _____ we are to reject the null hypothesis.
more likely
In order to use the normal distribution for interval estimation of μ when σ is known and the sample is very small, the population
must have a normal distribution
The mean of a binomial distribution is the product of
n and π
The standard deviation of the sampling distribution of the sample mean decreases when
n increases
When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals
n-1
In computing the standard error of the mean, the finite population correction factor is used when
n/N > 0.05
A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the
normal distribution
independence
observations in each sample are independent of each other
Type II error
occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation it means that the hypothesis test has failed to detect a real treatment effect
type I error
occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation it means the researcher concludes that a treatment does have an effect when in fact it has no effect
repeated measures design or within-subject design
one in which a single sample of individuals is measured more than once on the same dependent variable. the same subjects are used in all of the treatment conditions
The mean of the sampling distribution of p-hat is always = to
p
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p=< alpha
The purpose of statistical inference is to provide information about the
population based upon information contained in the sample
sampled population
population from which the sample is drawn
target population
population we want to make inferences about
Significance Level
predetermined threshold probability for determining if a test statistic is significant - if probability lower than the significance level, we can conclude that test statistic unlikely to have occurred by chance alone
The value of β gives the
probability of committing a Type II error
P-Value
probability, if H0 is true, of randomly drawing a sample like the one obtained or more extreme, in the direction of Ha
300 and 1
random samples of size 100 are taken from a population whose mean is mue=300 and standard deviation variance=10. The mean and standard error of the sample mean xbar, respectively, are:
Type I Error
rejecting the null hypothesis when, in fact, the null hypothesis was true
The probability distribution of the sample mean is called the
sampling distribution of the mean
normality
sampling error is distributed normally around the population mean in each treatment population
2.977
suppose that the sample mean and standard deviation are 10 and 3, respectively and the sample size is 15. To calculate the 99% confidence interval, you would then use a t-value of:
When s is used to estimate σ, the margin of error is computed by using
t distribution
Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?
t distribution
The t distribution is similar to the z distribution in all BUT one characteristics, which is that
t distribution's mean = 0 and standard deviation = 1
systematic sampling
taking every ___th element of pop. to sample. Because the first element selected is a random choice it is usually assumed to have the properties of a simple random sample. A form of probability sampling
1.960
the Z-value associated with a 95% confidence interval is:
t distribution
the complete set of t values computed for every possible random sample for a specific sample size or a specific degrees of freedom. Approximates the shape of a normal distribution
The sampling error is defined as
the difference between the value of a sample statistic and the value of the corresponding population parameter
homogeneity of variance
the distribution of error is the same for each population
population
the entire group of persons, places or items that we want to collect observations from is known as:
Null Hypothesis
the hypothesis that is directly examined by a statistical test
Given the sample size, the standard error of the mean (namely, the standard deviation of the distribution of all samples' means) will be larger,
the larger the standard deviation of the population from which the samples are taken is
The probability of rejecting a correct null hypothesis is ______ which is represented by the symbol _____.
the level of significance of a test; alpha
The mean of the sampling distribution of the sample mean is::
the mean of the means of all possible samples of the same size taken from the population
In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?
the mean of the population
For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is
the normal distribution
In hypothesis testing, the tentative assumption about the population parameter is
the null hypothesis
Whenever using the t distribution for interval estimation (when the sample size is very small), we must assume that
the population is approximately normal
Significance Level or Alpha (α) Level
the probability level below which a result is considered to be sufficiently unlikely to be due to chance. Typically α = .05 (i.e., 5 in 100). When p-value is lower than .05, the result is said to be statistically significant
Power
the probability of correctly rejecting the null hypothesis (Ho); that is, rejecting Ho when it is indeed false
Probability Value (p-value)
the probability that an outcome or one more extreme is due simply to chance
power of the statistical test
the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists
.6826
the random sample X is normally distributed with mean 10 and standard deviation 6. If n=36, compute the following probabilities: P(9 less than or equal to -xbar- less than or equal to 11) is:
.0228
the random sample X is normally distributed with mean 10 and standard deviation 6. If n=36, compute the following probabilities: P(xbar greater than or equal to 12) is:
.9987
the random sample X is normally distributed with mean 10 and standard deviation 6. If n=36, compute the following probabilities: P(xbar less than or equal to 13) is:
61
the sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is
In developing an interval estimate, if the population standard deviation is unknown
the sample standard deviation can be used
In interval estimation, the t distribution is applicable only when
the sample standard deviation is used to estimate the population standard deviation
sample statistics
the sampling distribution describes the distribution of
The probability distribution of a sample statistic is called
the sampling distribution of that statistic
Suppose we know that the mean age of all students at a university is 24 years. The mean age of a random sample of 100 students selected from this university is found to be 23.6 years. The difference 23.6-24=-.4 is called
the sampling error
The absolute value of the difference between the point estimate and the population parameter it estimates is:
the sampling error
The mean of the sampling distribution of the sample mean is:
the sampling error
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect
the size of the confidence interval to increase
standard error of the mean
the standard deviation of a sample distribution of the means is the
decreases as the sample size increases
the standard error of the sample mean xbar
directional hypothesis tes or one tailed test
the statistical hypotheses specify either an increase or a decrease in the population mean score. That is, they make a statement about the direction of the effect
the sample size is small
there is a large difference between (t sigma over 2) and (Z sigma over 2) when:
167
to estimate the mean of a normal population whose variance is 36, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of a least:
The mean of the sampling distribution of x- is always equal to
u
estimated standard error
used as an estimate of the real standard error when the value of the standard deviation is unknown. It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean and the population mean
t statistic
used to test hypothesis about an unknown population mean when the value of the standard deviation is unknown. The formula has the same structure as the z-score formula, except that the it uses the estimated standard error in the denominator
the population parameter
which of the following factors would not affect the width of a confidence interval?
In general, higher confidence levels provide
wider confidence intervals
sampling distribution of p ̄
x --- n
Super Clean Toothpaste manufacturing claims that they hold 26% of the toothpaste market. A study is designed to test the null hypothesis that p=.26 versus the alternative hypothesis that p ≠ .26. A sample of 800 elements selected from this population produced a sample proportion of .21 The value of the test statistic is:
z = -3.22
To compute a confidence interval, a ___ is used when the population standard deviation is known
z-statistic
Type I Error
α measures the probability of .....
decreases, type II Error
β ____ (increases/decreases) power. (β is AKA ____ ____ ____)
Type II Error
β measures the probability of .....
standard dev of x, infinite pop
σ ----- ⎷n
From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).
The sample size must be increased.
normal distribution
The sampling distribution of p ̄ can be approximated by a _________ ___________ whenever np≤ 5 and n(1-p) ≤ 5.
Statistics are used to report
The summary results of market surveys
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for each of the following
Y, N, Y, N
If the size of a sample equals the size of the population, the sample error is
Zero
The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal
Zero
sample standard deviation
___________ ⎷∑ (x-x ̄)^2 ------------ n-1
finite population correction factor
____________ ⎷ N-n / N-1
SRS infinite population
___________of size n from an infinite population is a sample selected such that the following conditions are satisfied. 1. Each element selected comes from the same population. 2. Each element is selected independently.
the parameter being estimated
a 95% confidence interval implies that we are confident 95 out of 100 that the constructed interval will include:
Alternative Hypothesis
a hypothesis that is contrary to the null hypothesis
effect size
a measure intended to provide an measurement of the absolute magnitude of a treatment effect, independent of the size of the sample being used
A Type II error is made when
a null hypothesis is rejected when it is actually false
A Type I error is made when
a null hypothesis is rejected when it is actually true
A population characteristic, such as a population mean, is called
a parameter
An interval estimate is a range of values used to estimate
a population parameter
alpha level or level of significance
a probability value that is used to define the very unlikely sample outcomes if the null hypothesis is true.
Independent measures or between-subjects design
a research design that uses a separate sample for each treatment condition or for each population
A subset of a population selected to represent the population is
a sample
SRS finite population
a sample size n from a finite population of size N, it is selected so that each possible sample of size n has the same probability of being selected.
The sampling distribution is the probability distribution of
a sample statistic
a random sample
a sample wherein all items in a population have the same chance of being selected for inclusion in the sample is
a probability distribution of x bar
a sampling distribution of the sample statistic x bar is
a point estimate
a single number sample statistic used to estimate a population parameter is
hypothesis test
a statistical method that uses sample data to evaluate a hypothesis about a population
A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for μ
becomes narrower
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller
When the level of confidence decreases, the margin of error
becomes smaller
As the confidence coefficient (CC) increases, the confidence interval
becomes wider
If the confidence level is increased, the interval for the population proportion
becomes wider
Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion
becomes wider
The sampling distribution of the proportion (namely, the distribution of the proportions, (p-hat s, of all samples) is approximately normal when
both np >= 5 and nq <= 5
The sampling distribution of p-hat is (approx) normal if
both np >= 5 and nq >=5
The significance level, denoted by α (alpha), is the probability of
committing a Type I error
Substantive Importance
concerned with estimated effect size. Only when knowing its effect size will we be able to interpret the meaning of our results - effect size refers to the magnitude of the result as it occurs in real life population (not laboratory)
The ability of an interval estimate to contain the value of the population parameter is described by the
confidence level
sampling with replacement
identifier from chosen element has been added back into frame and it could potentially be chosen a second time in the sample.
The critical value enables us to identify the rejection region in hypothesis testing
True
The wider the confidence interval is, the less precise is our estimate of the parameter
True
When computing weighted mean, the denominator is always the - of the -
-Sum -Weights
If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be
0.9
In a sample of 500 items produced by a machine, 7% are found to be defective. The 95% confidence interval for the proportion of defective items in all items produced by this machine is:
.048 to .092
A sample of 1000 families selected from a large city showed that 18% of them make $100,000 or more per year. The 99% confidence interval for the proportion of all families living in this city who make $100,000 or more per year is:
.149 to .211
the p-value must be a number between
0 and 1
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. What is the probability that a student scored 90 or higher?
0.0021
A group of statistics students conducts a survey at their university to find the mean amount of time students study per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?
0.0082
A true-false test consists of 6 questions. If you guess the answer to each question, what is the probability of getting all 6 questions correct?
0.016
The wildlife department has been feeding a special food to rainbow trout. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?
0.0222
Chances are 50-50 that a newborn baby will be a girl. For families with 5 children, what is the probability that all are girls?
0.031
80% of the trainees are female, 20% male. 90% of the females attended college, 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
0.08
The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the area under the normal curve between 400 and 482?
0.4495
What is the area under the normal curve between z = 0.0 and z = 1.79?
0.4633
On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for an in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?
0.599
A new computer game has been developed and 80 veteran game players will test its market potential. If 60 players liked the game, what is the probability that any veteran game player will like the new computer game?
0.75
Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. For a set of 4 tires, what is the probability that the average tire life is between 57,000 and 63,000 miles?
0.8664
A researcher wants to make a 95% confidence interval for the population mean. She wants the maximum error of estimate to be within 2.5 of the population mean. The population standard deviation is known to be 10.5o. The sample size that will yield a maximum error of estimate within 2.5 of the population mean is:
68
In terms of the standard error of the mean, how wide is a 99 percent confidence interval?
50152 standard errors
The number of students at a local university increased from 2,500 to 5,000 in 10 years. Based on a geometric mean, the university grew at an average percentage rate of
7.1% per year
A random sample of 85 group leaders and supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?
6.14 and 6.86
There are - experimental outcomes possible for the Binomial distribution
Two
If the variance is 3.6 grams, what is the standard deviation
1.897
The z value for a 95.0% confidence interval estimation is
1.96
A tire manufacturer advertises, "the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased 4 of these tires. What is the probability that all 4 tires will wear out before traveling 50,000 miles?
1/16 or 0.0625
What is the probability that a one-spot, two-spot, or six-spot will appear face up on the throw of one die?
1/2 or 0.5
A board of directors consists of 8 men and 4 women. A 4-member search committee is randomly chosen to recommend a new company president. What is the probability that all 4 members of the search committee will be women?
1/495 or 0.002
A researcher wants to make a 99% confidence interval for the population mean. She wants the maximum error of estimate to be within 4.8 of the population mean. The population standard deviation is known to be 18.65. The sample size that will yield a maximum error of estimate with in 4.8 of the population mean is:
101
The ages of the patients in the isolation ward of the hospital are 38, 26, 13, 41 and 22. What is the population variance?
106.8
The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?
13.9 and 14.1 inches
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the mean?
135 minutes
An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings which showed an average preparation time of 90 mins with a standard deviation of 140 min. What is the standard error of the mean?
14 Min
How many permutations of the letters C and D are possible
2
A student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit courses, Statistics a 4 credit course and Spanish a 3 credit course. If 4 grade points are assigned for an A, 3 for a B and 2 for a C, what is the weighted mean for the semester grades?
2.76
The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?
24/883 or 0.027
A new manufacturing process is implemented. The quality control division has no historic estimate for p. How large a sample should be taken to be 95% confident that the sample proportion is within .02 of the population proportion?
2401
A sample revealed the ages of a popular group of musicians are 36, 29, 37, 32, 36 and 75. What is the median age?
36
Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38 and 40. What is the mean deviation?
4.12
The top 10 football teams in the country, are to play every other team in the conference during the season and the team winning the most games would be the national champion. How many games would the conference commissioner have to schedule each year?
45
A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The population standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?
5.06 and 5.94
Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was 50,000 miles with a standard deviation of 3,500 miles. What is the estimated average tread life in miles for the entire population of these tires?
50,000
If a hypothesis test leads to the rejection of the null hypothesis,
A Type I error may have been committed.
A pie chart is similar to
A relative frequency distribution
If we test a small number of light bulbs from a large group, the small group is called
A sample
.0668
A sample of n=16 observations is drawn from a population with mean mue=1,000 and variance=200 Find the following probability: P(xbar greater than or equal to 1075) is:
.9772
A sample of n=16 observations is drawn from a population with mean mue=1,000 and variance=200 Find the following probability: P(xbar less than or equal to 1100) is:
.3413
A sample of n=16 observations is drawn from a population with mean mue=1,000 and variance=200 Find the following probability: P(xbar less than or equal to 950) is:
A sampling distribution is the probability distribution of
A sample statistic
Confidence interval
Interval estimation results in a ____ ____.
The scale used to measure a quantitative variable is either
Interval or Ratio
A population is a collection of
All individuals, objects, or measurements of interest
In determining the sample size needed to estimate a parameter, a researcher needs to
All of the above
The sample size needed to estimate a parameter is
All of the above
What measurement scale is used to measure unemployment?
Interval or ratio
The collection of one or more basic outcomes is called
An event
A random variable represents the outcomes of
An experiment
Statistically Significant
gauging probability of getting a certain result if there is no underlying (causal) effect
As the size of the sample increases, the shape of the distribution of sample means
Approaches a normal distribution
For a given confidence interval, what is the interpretation of a 96% confidence level?
Approximately 96 out of 100 intervals would include the true value of the population parameter
A statistic computed by summing all of the values of a distribution and dividing by the number of values is called
Arithmetic Mean
Type II Error
B is....
- theorem applies additional information to revise probabilities
Bayes'
Probability of success remains the same from trial to trial in - distribution
Binomial
A frequency polygon is a very useful graphic technique when
Comparing two or more distributions.
Type I Error
Concluding there is a significant difference, when in reality there is not.
Type II Error
Concluding there is no significant difference, when in reality there is.
point estimate, margin of error
Confidence intervals are composed of two values: a ____ ____ and a ____ ____ ____.
2
Consider a population with three observations: 1,2, and 3. If a sample of n=2 is randomly selected from this population with replacement: The mean of the sampling distribution of xbar, that is E(xbar) is:
1/3
Consider a population with three observations: 1,2, and 3. If a sample of n=2 is randomly selected from this population with replacement: The variance of xbar, var(xbar) is:
If an estimator tends to approach the value of the population parameter as the sample size increases, that estimator is said to be
Consistent
The performance of personal and business investments is measured as a percentage, "return on investment". What type of variable is "return on investment"?
Continuous
As the test statistic for an upper tail hypothesis test becomes larger, the p-value
gets smaller
The measures of dispersion Variance, Standard deviation & Mean deviation, are all based on
Deviations from the mean
What type of variable is the number of auto accidents reported in a given month?
Discrete
To convert a frequency distribution to a relative frequency distribution, you would
Divide each class frequency by the sum of the class frequencies
p
E(p ̄)=___
population mean
E(x ̄)=____
increases
Effect size ____ (increases/decreases) power.
convenience sampling
Elements are included in the sample without prespecified or known probabilities of being selected. For example, a professor conducting research at a university may use student volunteers to constitute a sample sim- ply because they are readily available and will participate as subjects for little or no cost. A form of non-probability sampling.
The midpoint of a class, or the class mark, is
Halfway between the lower and upper limits
larger
Higher confidence in a confidence interval means ____ (larger or smaller) margin of error.
50
In cases where the population is highly skewed or outliers are present, samples of size ____ may be needed.
Central Limit Theorem
In selecting random samples of size n from a population, the sampling distribution of the sample mean x ̄ can be approximated by a normal distribution as the sample size becomes large.
judgement sample
In this approach, the person most knowledgeable on the subject of the study selects elements of the popula- tion that he or she feels are most representative of the population. A form of non-probability sampling
Type II Error
Incorrectly accepting H_0
Type I Error
Incorrectly rejecting H_0
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
Increase the sample size.
What type of statistics is used when making an estimate/prediction
Inferential
The branch of statistics that uses sample info to make conclusions about a population is called
Inferential statistics
The - estimate states the range within which a population parameter probably lies
Interval
What level of measurement is the Centigrade temperature scale?
Interval
Which of the following best describes the form of the sampling distribution of the sample proportion?
It is approximately normal as long as np 5 and n(1-p) 5.
Which of the following best describes the form of the sampling distribution of the sample proportion?
It is approximately normal as long as np>= 5 and n(1-p) >= 5.
To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the population because
It is quicker
smaller
Larger sample size means ____ (larger or smaller) margin of error.
For any uniform probability distribution, the mean and standard deviation can be computed by knowing the
Maximum and minimum values of the random variable
The - measure of central location uses all of the observations in its calculation
Mean
The sum of the deviations of each data value from the - will always be zero
Mean
The measure of dispersion that disregards the algebraic signs (+ & -) of each difference between X and the mean is
Mean deviation
The standard error of the mean (namely, the standard deviation of the distribution of the samples' means)
Measures the amount of variation in the sampling distribution
For a data set, half of the observations are always greater than the
Median
The smallest measure of central location in a positively skewed distribution
Mode
The value that occurs most often in a set of data is the
Mode
The probability of rolling a 3 or 2 on a single die is an example of
Mutually Exclusive Events
To apply the special rule of addition, the events must be
Mutually exclusive
When the special rule of addition is used, the events must be
Mutually exclusive
number of n that can be selected from N
N! ----------- n!(N-n)!
People indicate their political party affiliation as Democrat, Republican or Independent. This data is what type of measurement?
Nominal
The lowest level of measurement is called
Nominal
There are 4 levels of measurement
Nominal, Ordinal, Interval & Ratio
Type I error plus Type II error
None of the above
Bell-shaped is a characteristic of the
Normal probability distribution
increases
Sample size ____ (increases/decreases) power.
The difference between a sample mean and the population mean is called
Sampling error
The - approach to probability is based on a person's belief, opinion or judgment
Subjective
The main purpose of descriptive statistics is to
Summarize the data in a useful and informative manner
α
Symbol for A is....
β
Symbol for B is....
The items or individuals of the population are arranged in a file drawer alphabetically by date received. A random starting point is selected and then every kth member of the population is selected for the sample. This sampling method is called
Systematic random sampling
___________ ⎷p(1-p)/n
That is, if the population is finite with n/N ≤ .05, we will use ________________.
Sampling a population is often necessary because
The cost of studying all the items in the population is prohibitive.
A sample of 20 items from a population with an unknown σ is selected in order to develop an interval estimate of μ. Which of the following is not necessary?
The sample must have a normal distribution.
A sampling error is
The difference between the value of a sample statistic based on a random sample and the value of the corresponding population parameter
An important similarity between uniform and normal probability distributions is
The mean and median are equal
The - diagram is useful when applying Bayes' Theorem
Tree
(T/F) The means x-bar s of 98% of samples will always be withing the probability interval [u-2.33(s/√N)] to [u+2.33(s/√N)]
True
Type II Error
The probability of accepting H_0 when it is false
Type I Error
The probability of rejecting H_0 when it is true.
To construct a binomial distribution, it is necessary to know
The total number of trials and the probability of success on each trial
An estimator said to be unbiased if the expected value of the statistic is equal to the value of the corresponding parameter.
True
sampling distribution of x ̄
The______________ ______________ ___ ___ is the probability distribution of all possible values of the sample mean x ̄.
Sample Size, Margin of Error
This formula helps us calculate the needed ____ ____ for a particular ____ ____ ____ (or E in this formula).
confidence interval, z
This formula is a ____ ____ for a ___ test.
confidence interval, t
This formula is a ____ ____ for a ____ test.
T/F If we take all possible samples, then 98% of the confidence intervals computed form samples, such as [x-bar-2.33(s/√N)]<u<[x-bar + 2.33(s/√N)] will extend wide enough to include the mean (u) of the populaton.
True
T/F The probability is 98% that the mean (x-bar) of any sample will be within the probability interval [u-2.33(s/√N)] to [u+2.33(s/√N)]
True
sample statistic
To estimate the value of a population parameter, we compute a corresponding characteristic of the sample, referred to as a ____________________.
A two-tailed test is a test with
Two rejection rejions
The error of rejecting a true null hypothesis is called ____ and the error of not rejecting a false null hypothesis is called _______.
Type I error; Type II error
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
Type II
estimation, point estimation, interval estimation
Unlike hypothesis testing, ____ uses sample statistics to approximate an exact value (____ ____) or a range of values (____ ____) for the population statistic.
To infer something about a population we
Usually take a sample from the population
In constructing a frequency polygon, class frequencies are scaled on what axis
Vertical axis
The hypothesis that defines the sampling distribution curve under which the area of α is displayed.
What is H0, the null hypothesis.
The hypothesis that defines the sampling distribution curve under which the area of ß is displayed.
What is Ha, the alternative hypothesis.
The change in ß when α is increased.
What is decreased.
sample mean
What is expected value of x ̄?
The change in power when sample size is increased.
What is increased.
The criteria we use to specify α.
What is seriousness of type I and type II errors.
The error made when a true null hypothesis is rejected.
What is type I error.
The error made when a false null hypothesis is not rejected.
What is type II error.
The probability of rejecting a false null hypothesis.
What is ß.
The largest risk a researcher is willing to take in rejecting a true null hypothesis.
What is α.
The probability of rejecting a true null hypothesis.
What is α.
unbiased
When the expected value of a point estimator equals the population parameter, we say the point estimator is _______________.
sampling without replacement
When we do not want and element to be selected twice so it is removed after the first time it is selected.
The null hypothesis claim:
about a population parameter that is assumed to be true until it is declared false
The alternative hypothesis claim:
about a population parameter that will be true if the null hypothesis is false
The sample mean is:
all of the above
The sample proportion is:
all of the above
Suppose we know that the mean weekly earnings of all employees of a company are $822. The mean weekly earnings of a random sample of 25 employees selected from this company is found to be $837. The difference 837 - 822 = 15 is called:
always equal to the population mean
Whenever the population has a normal probability distribution, the sampling distribution of x is a normal probability distribution for
any sample size
The Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of the proportion (namely, the distribution of the proportions, (p-hat, s) of all samples) will be ______ with its mean centered at ______ and its standard deviation equal to _______.
approx normal; p; sqrt(pq / n)
When the sample size is equal to or more than 30, the distribution of the samples' means will be ______ even though the population distribution may be extremely skewed.
approximately normal
The Central Limit Theorem states that regardless of the shape of the population distribution, the distribution of the samples' means will be ______, provided that the samples we take are ________
approximately normal; sufficiently large
cumulative density function
as the sample approaches infinite (positive infinite sign) most distributions will approach:
decreases
as the sample size n increases, the sampling error
As sample size (n) increases, the probability that the mean of a sample will be very far away from the mean of the population will:
decrease
As the sample size increases, the margin of error
decreases
How does the value of σ p̂ change as the sample size increases?
decreases
How does the value of σ x̄ change as the sample increases?
decreases
When n increases, the standard error of the mean (namely, the standard deviation of the distribution of all samples' means)
decreases
With a fixed sample size, as Type 1 error increases, Type II error
decreases
Degrees of freedom
describe the number of scores in a sample that are independent and free to vary
In a two-tailed test of hypothesis the two critical pointsL
divide the area under the sampling distribution of a sample statistic into two rejection and one nonrejection regions
In a one-tailed test of hypothesis, the critical point is a point that:
divides the area under the sampling distribution of a sample statistic into one rejection and one nonrejection regions
matched subjects study
each individual in one sample is matched with an individual in the other sample. The matching is done so that the two individuals are equivalent with respect to a specific variable that the researcher would like to control
cluster sampling
elements of population are divided into smaller groups, elements in groups are varied--like mini representations of larger pop. Samples are taken from different groups. A form of probability sampling
stratified random sampling
elements of the population are first divided into homogenous groups, then random samples are taken from each group. Smaller samples may be used with better accuracy. A form of probability sampling
Type II Error
failing to reject the null hypothesis when, in fact, it is false
Type II Error
failure to reject a false hypothesis
The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn form a population with a mean of mu and a standard deviation of s is:
sigma / sqrt(n)
The standard error of the mean (namely, the standard deviation of the distribution of all samples' means) is ___ the standard deviation of the population from which the samples are taken
smaller than
As the sample size increases, the
standard error of the mean decreases
null hypothesis
states that in the general population there is no change, no difference, or no relationship. In the context of an experiment it predicts that the independent variable has no effect on the dependent variable for the population
alternative hypothesis
states that there is a change, a difference, or a relationship for the general population. In the context of the experiment it predicts that the independent variable does have an effect on the dependent variable
it says the sampling distribution of xbar is approximately normal if n is large enough
suppose X has a distribution that is not normal. The Central Limit Theorem is important in this case because:
sample mean
∑ x ----- n
The sign in the alternative hypothesis in a two-tailed test is always
≠
