Statistics
The uniform probability distribution is used with
a continuous random variable.
Any process that generates well-defined outcomes is a(n)
experiment
For any continuous random variable, the probability that the random variable takes a value less than zero
is any number between zero and one.
The center of a normal curve
is the mean of the distribution.
Statistical inference
is the process of drawing inferences about the population based on the information taken from the sample.
For a uniform probability density function, the height of the function
is the same for each value of x.
The standard error of the estimate is the
square root of MSE.
As the sample size increases, the
standard error of the mean decreases.
The standard deviation of a point estimator is called the
standard error.
In a sample of 400 students in a university, 80 or 20% are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of
statistical inference.
The sample correlation coefficient shows a __ linear relationship between x and y.
strong positive
A method of assigning probabilities based upon judgment is referred to as the _____ method.
subjective
When s is used to estimate σ, the margin of error is computed by using the
t distribution.
The probability of committing a Type I error when the null hypothesis is true as an equality is
the level of significance.
The highest point of a normal curve occurs at
the mean.
The sum of frequencies for all classes will always equal
the number of elements in a data set.
The probability that Pete will catch fish when he goes fishing is .88. Pete is going to fish for 3 days next week. Define the random variable xto be the number of days Pete catches fish. The variance of the number of days Pete will catch fish is
0.3168., σ2=np(1−p)=3×0.88×(1−0.88)=0.3168
If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =
0.43., First, we know P(A∩B)=P(B|A)P(A)=0.4×0.35=0.14. Then, using the addition law, we know P(A U B)+P(A∩ B)-P(A)= 0.69+14-0.4=.43
For a standard normal distribution, the probability of z≤0 is
0.5
An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.25, and P(E3) = 0.05. The probability of outcome E4 is
0.5, The sum of the probabilities of all experimental outcomes is 1. Hence, P(E4) = 1 - P(E1) - P(E2) - P(E3) = 1 - 0.2 - 0.25 - 0.05 = 0.5.
For the standard normal probability distribution, the area to the right of the mean is
0.5.
If A and B are mutually exclusive events with P(A) = 0.25 and P(B) = 0.4, then P(A ∪ B) =
0.65.Because A and B are mutually exclusive, we know P(A∩B)=0. Using the addition law, we know P(A ∪ B)= P(A)+P(B)-P(A ∩B)= 0.25+0.4-0=.65
If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =
0.77, The addition law implies that P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.58 + 0.44 - 0.25 = 0.77.
Which of the following are continuous random variables? The weight of an elephant The time to answer a questionnaire The number of floors in a skyscraper The square feet of countertop in a kitchen
1, 2, and 4 only
A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is
1/(b - a).
The binomial probability distribution is used with a(n) _____ random variable.
discrete
A measure of the average value of a random variable is called a(n)
expected value.
A weighted average of the values of a random variable, where the probability function provides weights, is known as the
expected value.
The following data was collected from a simple random sample of a population. 13 17 18 21 23 The point estimate of the population mean
is 18.4.
The probability that a continuous random variable takes any specific value
is equal to zero
If a data set has an even number of observations, the median
is the average value of the two middle items.
The most frequently occurring value of a data set is called the
mode
Events that have no sample points in common are
mutually exclusive events.
If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are
mutually exclusive., A and B are mutually exclusive because P(A ∩ B) = 0. They are not independent because mutually exclusive events with non-zero probabilities cannot be independent. They are not complements of each other because P(A)+P(B)≠1.
When developing an interval estimate for the difference between two population means with sample sizes of n1 and n2,
n1 and n2 can be of different sizes.
are labels used to identify attributes of elements.
only with quantitative data.
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p-value<= α.
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in one hour is 31.8. Which of the following discrete probability distributions' properties are satisfied by random variable x?
poisson
When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a _____ distribution.
poisson
μ is an example of a
population parameter.
If the null hypothesis is not rejected at the 1% level of significance, it _____ rejected at the 5% level
will sometimes be
The population being studied is usually considered _____ if it involves an ongoing process that makes listing or counting every element in the population impossible.
infinite
When n - 1 is used in the denominator to compute variance, the data set
is a sample.
Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.
matched, independent
The measure of location which is the most likely to be influenced by extreme values in the data set is the
mean
The sampling distribution of p¯1−p¯2 is approximated by a normal distribution if _____ are all greater than or equal to 5.
n1p1, n1(1 - p1), n2p2, n2(1 - p2)
For a continuous random variable x, the height of the function at x is
named the probability density function f(x).
The shape of the sampling distribution of p¯ is ____ distribution.
normal
The sampling distribution of p¯1−p¯2 is approximated by a
normal distribution.
The sum of the relative frequencies for all classes will always equal
one.
An infinite population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean?
pic q3
When the data are skewed to the right, the measure of Skewness will be
positive.
A description of the distribution of the values of a random variable and their associated probabilities is called a
probability distribution.
A graphical presentation of the relationship between two quantitative variables is a
scatter diagram
When the population has a normal distribution, the sampling distribution of is normally distributed for any sample
size
In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then
the estimated regression line intercepts the positive y-axis.
A negative value of z indicates that
the number of standard deviations of an observation is to the left of the mean.
The collection of all elements of interest in a study is
the population.
If two events are independent, then
the product of their probabilities gives the probability of their intersection.
A cumulative relative frequency distribution shows
the proportion of data items with values less than or equal to the upper limit of each class.
The collection of all possible sample points in an experiment is
the sample space.
Consider a uniform distribution ranging between 1 and 6. The probability density function for a value between 1 and 6 is
0.2.f(x)=1/b−a=1/6−1=0.2.
x is a normally distributed random variable with a mean of 7 and a standard deviation of 2. The probability that x is between 6.48 and 7.56 is
0.2128., P(6.48≤x≤7.56)=P(6.48−7/2≤z≤7.56−7/2)=P(z≤0.28)−P(z≤−0.26). Checking the standard normal probability table, we find that P(z≤0.28)=0.61026and P(z≤−0.26)=0.39743. Hence, P(6.48≤x≤7.56)=0.61026−0.39743=0.21283.
If A and B are independent events with P(A) = 0.5 and P(A ∩ B) = 0.12, then, P(B) =
0.24., If A and B are independent events, then we know P(A)P(B) = P(A ∩ B). This implies that P(B) = P(A ∩ B)/P(A) = 0.12/0.5 = 0.24.
If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =
0.68, Because A and B are independent, we know P(A∩B)=P(A)P(B)=0.2×0.6=0.12. Then, the addition law implies that P(A∪B)=P(A)+P(B)−P(A∩B)=0.2+0.6−0.12=0.68.
Events A and B are mutually exclusive with P(C) = 0.35 and P(B) = 0.25. Then, P(Bc) =
0.75, P(Bc) = 1 - P(B) = 1 - 0.25 = 0.75.
Michael is running for president. The proportion of voters who favor Michael is 0.8. A simple random sample of 100 voters is taken. Assume the total number of voters is large. What is the expected value of the sampling distribution of p¯? (round to the nearest thousandth)
0.8 (with margin: 0) The mean of the sample proportion equals the population proportion.
z is a standard normal random variable. The P(−1.96≤z≤1.4)equals
0.8942.P(−1.96≤z≤1.4)=P(z≤1.4)−P(z≤−1.96). Checking the standard normal probability table, we find that P(z≤1.4)=0.91924 and P(z≤−1.96)=0.02500. Hence, P(−1.96≤z≤1.4)=0.91924−0.02500=0.89424.
x is a normally distributed random variable with a mean of 24 and a standard deviation of 6. The probability that x is less than 12 is
0.9772.P(x≤12)=P(z≤12−24/6)=P(z≤−2). Checking the standard normal probability table, we find that P(z≤−2)=0.02275.
Read the t statistic from the t distribution table and choose the correct answer. For a two-tailed test with a sample size of 20 and using α = .20, the critical value tα/2=
1.328 Degree of freedom is 19 t(α/2)=1.328
A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. What is the expected value of the sampling distribution of the sample mean? (round to the nearest thousandth)
10.5 (with margin: 0.001) The mean of the sample mean equals the sample mean.
In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to
100
An experiment consists of selecting a student body president and vice president. Four students are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
12, In this question, we are selecting 2 out of 4 alternatives and the order of selection matters. Therefore, the total number of sample points is P24=4!/(4−2)!=12.
From a group of six people, two individuals are to be selected at random. How many selections are possible (assuming the order of selection does not matter)?
15, In this question, we are selecting 2 out of 6 alternatives and the order of selection does not matter. Therefore, the total number of sample points is C26=6!/2!(6−2)!=15.
A group of students had dinner at a local restaurant. The total bill for the dinner was $364.99. Each student paid his/her equal share of the bill, which was $21.47. How many students were at the dinner?
17
Random variable x has the probability function f(x) = X/6, for x = 1, 2 or 3. The expected value of x is
2.333.. μ=∑xf(x)=1/6×1+2/6×2+3/6×3=2.333.
The probability that Pete will catch fish when he goes fishing is .88. Pete is going to fish for 3 days next week. Define the random variable xto be the number of days Pete catches fish. The expected number of days Pete will catch fish is
2.64.μ=np=3×0.88=2.64
The standard deviation of a sample of 81 observations equals 49. The variance of the sample equals
2401
The first quartile is the same as the
25th percentile
(b) How many variables are in this data set?
3
An experiment consists of three steps. There are five possible results on the first step, two possible results on the second step, and three possible results on the third step. The total number of experimental outcomes is
30, The total number of experimental outcomes is 5×2×3=30
Assume that you have a binomial experiment with p = 0.4 and a sample size of 150. The variance of this distribution is
36, The variance of a binomial distribution is given by np(1 - p) = 150×0.4×(1−0.4)=36.
The use of the normal probability distribution as an approximation of the sampling distribution of p¯ is based on the condition that both npand n(1 - p) equal or exceed
5
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in one hour is 31.8. The variance of the random variable x is
5.3., For a Poisson distribution, σ^(2)=μ=5.3.
A simple random sample of 100 observations was taken from a large population. The population mean and standard deviation were determined to be 50 and 5, respectively. The standard error of the mean is
The random sample is taken from a large population. Therefore, we should use the formula for the standard deviation of x¯, for an infinite population, σx¯=σ/sqrt(n). We know σ=5 and n=100. Hence, σx¯=5/sqrt(100)=0.5.
The number of customers that enter a store during one day is an example of
a discrete random variable.
A standard normal distribution is a normal distribution with
a mean of 0 and standard deviation of 1.
The height of a person is an example of
a quantitative variable.
A normal distribution with a mean of 0 and a standard deviation of 1 is called
a standard normal distribution.
A cumulative frequency distribution is
a tabular summary of a set of data showing sums of frequencies.
The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the rule for
combinations
The ability of an interval estimate to contain the value of the population parameter is described by the
confidence level
A random variable that may take on any value in an interval or collection of intervals is known as a _____ random variable.
continuous
The entities on which data are collected are
elements
The model developed from sample data that has the form of y^=b0+b1x is known as the
estimated regression equation
The model developed from sample data that has the form of y^=b0+b1x is known as the
estimated regression equation.
Which difficulty of range as a measure of variability is overcome by interquartile range?
The range is influenced too much by extreme values
Given that z is a standard normal random variable, what is the value of zif the area to the left of z is 0.2358?
-0.72, From the question, we know P(z≤z0)=0.2358. Checking the standard normal probability table, we know z0=−0.72.
What is the probability that x is between 4 and 8, given the probability density function below?
0.23865, This is an exponential distribution with μ=8. Hence, P(4≤x≤8)=e^(−4/8)−e^(−8/8)=0.60653−0.36788=0.23865.
Select the variables that are categorical.
Condition
Which of the following types of data cannot be appropriately displayed by a histogram?
Cumulative frequency
Select the variables for which arithmetic operations are appropriate.
Hi, Lo
Which of the following statements is always true? I. −0.5≤P(Ei)≤0.5. II. P(A)=1−P(A^C). III. P(A)+P(B)=1. IV. ∑Pi>1.
II
In computing the standard error of the mean, the finite population correction factor is used when
N/n > 0.05., A finite population is treated as being infinite if and only if n/N <= 0.05. Hence, it is not treated as being infinite if n/N > 0.05.
Events A and B are mutually exclusive. Which of the following statements is also true?
P(A ∪ B) = P(A) + P(B)
Given that z is a standard normal random variable, what is the probability that z≥−2.12
P(z≥−2.12)=1−P(z≤−2.12). Checking the standard normal probability table, we find that P(z≤−2.12)=0.01700. Hence, P(z≥−2.12)=1−0.01700=0.98300.
In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the _____ distribution
Poisson
Which of the following does not need to be known in order to compute the p-value?
The level of significance
Which of the following is not a property of a binomial experiment?
The probabilities of the two outcomes can change from one trial to the next.
What is the probability that x is less than 6, given the probability density function below?
This is an exponential distribution with μ=8. Hence, P(x≤6)=1−e^(−6/8)=1−0.47237=0.52763.
The Poisson probability distribution is a _____ probability distribution.
discrete
A characteristic of interest for the elements is called a
variable
The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.
point estimate, margin of error
The range of probability values is
0 to 1
If A and B are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =
0, If A and B are mutually exclusive, then P(A∩B)=0. Hence, P(A|B)=P(A∩B)/P(B)=0.
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =
0, When two events are mutually exclusive, the probability of their intersection is zero.
The random variable x is known to be uniformly distributed between 50 and 90. The probability of x having a value between 70 to 80 is
0.25, P(70≤x≤80)=d−c/b−a=80−70/90−50=0.25.
Which of the following is not a characteristic of the normal probability distribution?
99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
In order to test the following hypotheses at an α level of significance H0: μ <= 800 Ha: μ > 800 the null hypothesis will be rejected if the test statistic z is
>=zα, This is upper tail hypothesis testing. As a result, the null hypothesis should be rejected if the test statistic z >=zα. Where zα is the cutoff value such that P(z>=zα) = α .
Which of the following is correct?
SST = SSR + SSE
Which of the following is a characteristic of the standard normal probability distribution?
The standard deviation must be 1
Each individual outcome of an experiment is called
a sample point.
A continuous random variable may assume
all values in an interval or collection of intervals.
An unusually small or unusually large data value is called
an outlier
A continuous random variable may assume
any numerical value in an interval or collection of intervals.
If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means
can be approximated by a normal distribution.
For the following hypothesis test, H0: μ ≥ 150 Ha: μ < 150 the test statistic
can be either negative or positive.
If the coefficient of determination is a positive value, then the coefficient of correlation
can be either positive or negative.
A normal probability distribution
can have mean of any numerical value.
Two events with nonzero probabilities
can not be both mutually exclusive and independent.
The coefficient of determination
cannot be negative.
The standard deviation of a normal distribution
cannot be negative.
For ease of data entry into a university database, 1 denotes that the student is a freshman, 2 indicates a sophomore, 3 indicates a junior, and 4 indicates that the student is a senior. In this case, data are
categorical
In a questionnaire, respondents are asked to mark their marital status as single, married, divorced, or widowed. Marital status is an example of a(n) _____ variable.
categorical
A numerical measure of linear association between two variables is the
covariance
Data collected at the same, or approximately the same point in time are _____ data.
cross-sectional
Facts and figures that are collected, analyzed and summarized for presentation and interpretation are
data.
A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: y^=9−4x The above equation implies that if the price is increased by $1, the demand is expected to
decrease by 4000 units.
In regression analysis, the variable that is being predicted is the
dependent variable.
In a sample of 800 students in a university, 240 or 30% are Business majors. The 30% is an example of
descriptive statistics.
Statistical studies in which researchers control variables of interest are _____ studies.
experimental
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) _____ probability distribution.
exponential
If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n) _____ probability distribution.
exponential
For a continuous random variable x, the probability density function f(x)represents the
height of the function at x.
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: y^=40−6x The above equation implies that an
increase of $1 in price is associated with a decrease of $6000 in sales.
When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____ samples.
matched
Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on
matched samples
The intersection of two mutually exclusive events
must always be equal to 0.
A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .02. The null hypothesis
must be rejected, Here p-value = 0.02 and α=0.05. As p-value ≤ α, the null hypothesis should be rejected.
The shape of the sampling distribution of the sample mean is ____ distribution.
normal
The expected value for a binomial distribution is given by equation
np
The variance Var(x) for the binomial distribution is given by equation
np(1 - p)
Statistical studies in which researchers do not control variables of interest are _____ studies.
observational
The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called the counting rule for
permutations.
The function that defines the probability distribution of a continuous random variable is a
probability density function.
Sampling distribution of x¯ is the
probability distribution of the sample mean.
Sampling distribution of p¯ is the
probability distribution of the sample proportion.
A numerical description of the outcome of an experiment is called a
random variable.
The difference between the largest and the smallest data values is the
range
The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as the
regression equation.
In regression analysis, the model in the form y=β0+β1x+ϵ is called the
regression model.
A tabular summary of a set of data showing the fraction of the total number of items in several classes is a _____ distribution.
relative frequency
When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the _____ method.
relative frequency
The coefficient of variation is the
standard deviation divided by the mean times 100.
The standard error of the difference between two sample means, x¯1−x¯2, is the
standard deviation of the sampling distribution of the difference.
A numerical value used as a summary measure for a sample is known as a sample
statistic.
The interquartile range is
the difference between the third quartile and the first quartile.
If two variables, x and y, have a strong linear relationship, then
there may or may not be any causal relationship between x and y.
In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as a _____ line.
trend
In hypothesis tests about p1 - p2, the pooled estimator of p, p¯, is a(n)
weighted average of the two sample proportions.
If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =
0.21, The addition law states that P(A ∪ B) = P(A) + P(B) - P(A ∩ B). It implies that P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.62 + 0.47 - 0.88 = 0.21.
The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals
24.
What is the mean of x, given the probability density function below? f(x)= 1/8e^(-x/8)
8, This is an exponential distribution with μ=8
Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is
8, We know this is a binomial distribution with n = 400 and p = 0.2. Then, the variance is give by np(1 - p) = 400×0.2×(1−0.2)=64. Hence, the standard deviation is 64=8.
What type of error occurs if you reject H0 when, in fact, it is true?
A Type I error is rejecting H0 when it is true. A Type II error is accepting H0 when it is false
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in one hour is 31.8. The probability that there are 8 occurrences in ten minutes is
.0771., .The number of occurrences in ten minutes follows a Poisson distribution with μ=5.3. Therefore, the probability that there are 8 occurrences in ten minutes is given by f(x)=μ^(x)e^(−μ)/x!=5.3^(8)e^(−5.3)/8!=0.0771.
Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using α = .0901, the critical value −zα =
-1.34, We are looking for the critical value such that P(z<=critical value) = 0.0901.
Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (lower tail), using a sample size of 14, and at the 5% level of significance, critical value −tα=
-1.771, Read the t-distribution table. Degree of freedom = n-1=13 -tα=-1.771 for lower tail test, the critical value we use is
A production process produces 2.5% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
0.0058, The number of defective parts in the sample has a binomial probability distribution. The number of trials is n = 5. The probability of successes is p = 0.025. Therefore, the probability that the sample contains exactly two defective parts is given by n!/x!(n−x)!p^(x)(1−p)^(n−x)=5!/2!(5−2)!0.025^(2)(1−0.025)^(5−2)=0.0058
If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∩ B) =
0.1., Because A and B are independent, we know P(A∩B)=P(A)P(B)=0.4×0.25=0.1
What is the probability that x is larger than 10, given the probability density function below?
0.28650, This is an exponential distribution with μ=8. Hence, P(x>_10)=e^(10/8)=0.28650
The number of observations in a complete data set having 15 elements and 5 variables is
15
The point estimate of the population standard deviation is
3.847
The hourly wages of a sample of 130 system analysts are given below. mean = 60 range = 20 mode = 73 variance = 324 median = 74 The coefficient of variation equals?
30%
(c) How many observations are in this data set?
7
A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?
If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
The z value for a 97.8% confidence interval estimation is
In this question, 1−α=0.978, which means α=0.022. Then, zα2 is the (1−0.022/2)×100=98.9th percentile of the standard normal distribution, which equals 2.29.
A student's dormitory room number is an example of
a categorical variable.
The exponential probability distribution is used with
a continuous random variable.
The weight of an object is an example of
a continuous random variable.
In statistical experiments, each time the experiment is repeated
a different outcome might occur.
In the following estimated regression equation y^=b0+b1x
b1 is the slope.
Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion
becomes wider
The correlation coefficient ranges between
-1 and +1.
If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A | B) =
.38, If A and B are independent, then P(A) = P(A|B) = 0.38.
For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is
.5, For lower tail hypothesis testing, p-value = P(z<= test statistic)=P(z<= 0) = 0.5
A random sample of 64 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is
18.8 to 21.2., The standard error is given by σx¯=σ/sqrt(n)=4.8/sqrt(64)=4.88=0.6.. In this question, 1−α=0.9544, which means α=0.0456. Then, zα2 is the (1−0.0456/2)×100=97.72th percentile of the standard normal distribution, which equals 2. The marginal of error is then given by zα/2(σx¯)=2×0.6=1.2. Hence, the 95.44% confidence interval is (20 - 1.2,20 + 1.2) = (18.8,21.2).
The standard deviation of a sample was reported to be 20. The report indicated that ∑(x−x¯)2= 7200. What is the sample size?
19
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the
coefficient of determination.
The area of the continuous uniform probability distribution is
rectangular
Five hundred residents of a city with a population of 240,495 are polled to obtain information on voting intentions in an upcoming city election. The five hundred residents in this study is an example of a(n)
sample
The absolute value of the difference between the point estimate and the population parameter it estimates is the _____ error.
sampling
Random samples of size 600 are taken from an infinite population whose population proportion is 0.4. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is
0.0200. The random sample is taken from an infinite population. Therefore, we should use the formula for the standard deviation of p¯, for an infinite population, σp¯=sqrt(p(1−p)/n). We know p=0.4and n=600. Hence, σp¯=sqrt(0.4×0.6/600)=0.02.
If P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88, then P(B | A) =
0.04, The addition law states that P(A ∪ B) = P(A) + P(B) - P(A ∩ B). It implies that P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.5 + 0.4 - 0.88 = 0.02. Hence, we know P(B|A) = P(A∩B)P(A)=0.020.5=0.04
In a two-tailed hypothesis test situation, the population standard deviation is unknown. We know the test statistic is determined to be t= -2.032. The sample size is 35. The p-value for this test is
0.05, Sample size n = 35 and Degree of freedom is n-1 = 34. Check the t-distribution table P(t<=-2.032) = P(t>=2.032) = 0.025 (area in Upper tail) Two tail test: p-value = 2*P(t<=-2.032) = 0.05
x is a normally distributed random variable with a mean of 6 and a variance of 4. The probability that x is greater than 8.75 is
0.0838, P(x≥8.76)=P(z≥8.76−6/sqrt(4))=1−P(z≤1.38). Checking the standard normal probability table, we find that P(z≤1.38)=0.91621. Hence, P(x≥8.76)=1−0.91621=0.08379.
If a coin is tossed three times, the likelihood of obtaining three heads in a row is __., (Assign probabilities using the classical method.)
0.125, This is a 3-step experiment with each step having two possible results. Therefore, there are, in total, 2×2×2=8experimental outcomes. It means that the probability of seeing any particular outcome, such as three heads in a row, equals 1/8 = 0.125, if we assign probabilities using the classical method.
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in one hour is 31.8. The expected value of the random variable x is
5.3., We know the expected value of occurrences in an interval is proportional to the length of the interval if the number of occurrences follows a Poisson distribution. Then, because the mean number of occurrences in one hour (which is 60 minutes) is 31.8, we know the mean number of occurrences in ten minutes is 31.8/60×10=5.3.
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?
50%, For any normal random variable x, the probability that x is larger (smaller) than its mean is 50%.
The median of a sample will always equal the
50th percentile.
It is known that the population variance (σ2) is 125. At 95% confidence, what sample size should be taken so that the margin of error does not exceed 3?
54,
A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. If we want to provide a 95% confidence interval for the population mean SAT score, the degree of freedom for reading the t value is
63
The following shows the temperatures (high, low) and weather conditions on a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy. picture 21, (a) How many elements are in this data set?
7
Given that z is a standard normal random variable, what is the probability that z≤1.46
Checking the standard normal probability table, we find that P(z≤1.46)=0.92785
Which of the following is a measure of variability?
Interquartile range
Whenever the population has a normal probability distribution, the sampling distribution of x¯ is a normal probability distribution for
any sample size.
The continuous uniform, normal, and exponential distributions
are all continuous probability distributions.
Quantitative data
are always numeric.
Categorical data
are labels used to identify attributes of elements.
A probability distribution showing the probability of x successes in ntrials, where the probability of success does not change from trial to trial, is termed a
binomial probability distribution.
A survey to collect data on the entire population is a(n)
census.
The difference between consecutive lower class limits of adjacent classes provides the
class width.
When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the _____ method.
classical
If there is a very weak correlation between two variables, then the coefficient of determination must be
closer or equal to zero, The coefficient of determination is the square of the correlation coefficient.
If there is a very weak correlation between two variables, then the coefficient of determination must be
closer or equal to zero.
In simple linear regression, r2 is the
coefficient of determination.
The __________ can be interpreted as the number of standard deviations a data value is from the mean of all the data values.
z-score
