MATH 2228 Quizzes Macleod
A die is rolled 25 times and an even number appears on 12 of those rolls. What is the proportion of even-numbered rolls in that sample of 25 (p̂)?
0.48
A given Binomial problem is one where the normal distribution must be used to approximate the probabilities. To find P(X > 65), which value would you use to change to z?
65.5
If a child is at the 80th percentile (P80) in height, this means which of the following?
80% of the children his age are as tall or shorter than he is.
The five-number summary for a set of test scores is given below: 32 68 74 82 96 Which score corresponds to the third quartile (Q3)?
82
When using the Empirical Rule with a set of data, what percent of the values lies within 3 standard deviations of the mean?
99.7%
Which license do you use when building a confidence interval for a proportion if the sample size is 60?
D
When a probability question concerns a proportion from a sample, which 'license' would be used to give 'permission' to use the normal (z) table?
D, if np and nq are both at least 5
Which of the following licenses is not used when building a confidence interval?
E
Which 'license' will give you 'permission' to find Binomial probabilities using the normal (z) table?
E, if np and nq are both at least 5
In an hypothesis test, if the p-value is less than .05, which conclusion should be reached?
H0 should be rejected and Ha is supported .
If two events are known to be independent, ALL BUT ONE of the following statements would be true. Which one is NOT true?
P(A U B) = P(A) + P(B)
If two events are NOT mutually exclusive, which of the following formulas would you use to find P(A U B).
P(A) + P(B) - P(A ∩ B)
When using the four-step process to check whether two events A and B are independent, which two values should be compared?
P(A) and P(A|B)
To calculate the conditional probability that an event K would occur given that event C has occurred, which of the following would be the appropriate formula to use?
P(K | C) = P (K n C) / P (C)
Which of the following is NOT true for a continuous probability distribution?
P(X = 6) changes from distribution to distribution.
Which of the following is true of Binomial distributions?
Some Binomial distributions are normal in shape.
The uniform distribution is an example of which type of probability distribution?
continuous
The Binomial distribution is which of the following?
discrete
Licenses A and B can always be used interchangeably.
false
Suppose 15% of the students in a high school are left-handed. In a sample of 10, it is desired to know what the probability is that between 3 and 6 of them are left-handed. To use the Binomial tables, you would do which of the following?
go the column where n=10, p=.15, and add the probabilities for x values of 4, 5
When calculating the expected value for a discrete random variable, the result is often a decimal value. It is not possible for there to be 8.3 people or 15.71 cars. When the result is a decimal, what should you do?
leave the values as they are with the decimals, so the expected values would be 8.3 people and 15.71 cars for the given problems
Which of the following is true of hypothesis tests concerning proportions?
they can be either one- or two-tailed
Which of the following is to be expected when building a confidence interval for a mean?
to estimate the value of a population mean that is unknown
A market researcher is interested in determining the average income for families in Pitt County, North Carolina. To accomplish this, she takes a random sample of 400 families from the county and uses the data gathered from them to estimate the average income for families of the entire county. This process is an example of _______.
inferential statistics
500 randomly selected ECU students were surveyed and 20% said they were left-handed. From this it is concluded that the probability of an ECU student being left-handed is .20. This is an example of which type of probability assignment?
long-term/large scale relative frequency
In order to use the normal table you must have a z-score. In order to find a z-score, you need which two values?
mean and standard deviation
If a dog has a shorter-than-average tail length, its tail length would have a z-score that is which of the following?
negative
In a given normal distribution the mean is 30. If you are asked to find the probability of getting a value that is greater than 24, you would expect the z-score to be which of the following?
negative
A qualitative variable could also be described as continuous.
never
In a voluntary response survey, when predominantly those with negative opinions respond to a questionnaire, while only a few of those with positive or neutral opinions respond, this is an example of which of the following?
non-response bias
In both the class samples and the simulation samples for the dice rolling exercise, when all samples were combined into a single distribution, what was the overall shape of the distribution?
normal
Which Binomial method uses the list/sweep/half-unit procedure?
normal approximation
When asked to find P(Ac), the 'little c' is translated as which of the following?
not
When asked to find P(A U B), the symbol U is translated as which of the following?
or
When using the formula to determine sample size with a 95% level of confidence, what values should be used for p and q when no planning value from a similar study is available?
p = .5 and q = .5
Which of the following is NOT an example of non-sampling error?
standard error
When sample data is used to estimate a population parameter that is not obtainable, this is an example of which of the following?
statistical inference
The graph of a Binomial distribution consists of which of the following?
sticks
Below are several potential characteristics of a chair in someone's living room. Which two would be mutually exclusive? solid color cloth fabric recliner striped rocker
striped and solid color
To create a sampling distribution, you start by doing which of the following?
taking lots of samples of the same size from the same population
Which of the following does the Central Limit Theorem guarantee?
that a sampling distribution will be normal if the sample size used is large
The first quartile (Q1) for a set of data is the same as which of the following?
the 25th percentile (P25)
The values on the interior region of the normal (z) table correspond to which of the following?
the area to the left of a given z value on both sides of the table
Which of the following is a qualitative variable?
the brand of motor oil purchased
The term 'standard deviation' for a data set indicates a typical deviation from which value?
the mean
A given Binomial problem is one where the normal distribution must be used to approximate the probabilities. To determine the mean and standard deviation needed to calculate a z-score, which of the following is the case?
the problem will provide information that can be used to calculate the mean and standard deviation
What is the feature in a confidence interval (mean) problem that indicates use of 'degrees of freedom' is necessary?
the standard deviation is from a sample
Which of the following is the function of the process of regression?
to formulate the best possible linear equation to model the relationship between two variables
The scores on a test are normally distributed and have a mean of 78 and a standard deviation of 9. If you are asked to find the probability that a sample of 12 students has a mean score that is at least 80, which distribution would you use?
x̅ sampling distribution
Suppose the probability that a first grader can ride a bike is .53. Three first graders are selected at random. Independence from one child to the next may be assumed. What is the probability that all 3 of them can ride a bike?
0.149
In a Binomial distribution, where the sample size is 12 and the probability of a success is .85, what is the value of q?
0.15
Which of the following could NOT be a p-value?
1.5
In a population of items, 36% of them have a certain characteristic. If a random sample of 12 of these items is taken, which of the following calculations would you perform to determine how many of them you would expect to have this characteristic?
12(.36)
For a Binomial problem, which values would be of interest when finding P(16 < X < 22)?
17, 18, 19, 20, 21
When constructing a 98% confidence interval, what value of z would be used in the calculation?
2.326
Use the nCr function on your calculator to find (10 4)
210
For a Binomial problem, which values would be of interest when finding P(24 < X < 30)?
25, 26, 27, 28, 29
For a Binomial problem, which values would be of interest when finding P(35 < X < 42)?
36, 37, 38, 39, 40, 41
In a pie chart, the degree measures of the angles must total to which of the following?
360
Which of the following is NOT true of a normal distribution?
About 95% of the data is within 1 standard deviation of the mean.
If a child's height (in inches) has a z-score of 1.5, this means which of the following?
The child's height is 1.5 standard deviations above the mean for his/her age group.
Suppose that the equation for the line of best fit for two variables is determined to be: ŷ = 42 + 6x. Which of the following is a true statement?
The slope of the line is 6.
Controlled experiments can determine whether there is a cause/effect relationship between two variables.
True
In a histogram, the bars on the graph share sides.
True
No mutually exclusive events are independent.
True
Observational studies cannot determine whether there is a cause/effect relationship between two variables.
True
P(A U B) = P(B U A)
True
P(A ∩ B) = P(B ∩ A)
True
P(Ac) = 1 - P(A)
True
The total area is one.
True for continuous
The distribution is symmetric and extends infinitely in both directions.
True for normal distribution
The standard deviation determines the width of the curve.
True for normal distribution
In an hypothesis test, which type of error is possible if the data leads you to reject H0 ?
Type I
Which of the following describes a PARAMETER?
a measured characteristic of a population
In an experiment, which of the following refers to the need for having a group that does not receive the experimental treatment in order to have a basis for comparison?
control
When determining a sample size, when should degrees of freedom be used?
degrees of freedom should never be used
Which of the following is true when building a confidence interval for a proportion?
degrees of freedom will never be used
There are pre-existing mathematical formulas, relating one variable to another, that are scientifically proven to work in all circumstances (like d = rt). These formulas are examples of which of the following?
deterministic models
The median is resistant to outliers.
True
The value of Sxx is always positive.
True
Probability for an interval is found by determining the area under the graph in the interval.
True for continuous
The graph is a density curve, as opposed to sticks or bars.
True for continuous
The mean can be positive, negative, or zero.
True for normal distribution
The mean, median, and mode are all the same value.
True for normal distribution
Which of the following variables is discrete?
# of dogs visiting a vet's office daily
Suppose 10% of the students in a high school are left-handed. In a sample of 15, it is desired to know what the probability is that exactly 4 are left-handed. Which of the following is the correct calculation for this probability?
(15 4) (.10^4) (.90^11)
In a two-tailed hypothesis test, if the area in the upper tail is found to be .0126, what would be the p-value?
.0252
In a sample of 80 college students, 52 of them have a dog. What proportion of the sample has a dog?
.65
In a confidence interval problem where it is necessary to use 'degrees of freedom' and where the sample size is 20, how many degrees of freedom would be needed?
19
The primary tell-tale feature of a Binomial variable is that there are _____ outcomes possible for each person/item sampled.
2
In a 95% confidence interval problem where it is necessary to use 'degrees of freedom' and where the sample size is 15, what value of t would be used to build the interval?
2.145
Which 2 Binomial probability methods do NOT require a license?
Binomial formula and Binomial tables
In a Binomial probability problem, if the nature of the problem is such that it is feasible to use either the Binomial tables or the normal distribution to approximate the probability, which would give the more accurate answer?
Binomial tables
Which method would be most appropriate to use if you are calculating a Binomial probability and the probability question concerns a percent?
p̂ sampling distribution
The coefficient of determination is represented by which of the following variables?
r^2 r2
Which one of the following does NOT give equivalent names for the same variable?
response, x
To estimate the proportion of adults over 60 who exercise regularly, a random sample of 30 adults over 60 is selected. In that sample, 18 responded that they do exercise regularly. To use this information to construct a 90% confidence interval for the proportion of all adults over 60 who exercise regularly, which of the following formulas would be used?
.60 ± 1.645 (σp̂)
For a data value that is 1.05 standard deviations above the mean, what area reading does this correspond to from the normal (z) table?
.8531
A test is timed for 20 minutes. Let X = the time a student took to take the test. The possible values for the variable would be given by which of the following?
0 ≤ X ≤ 20
If the variance for a set of values is 36, which of the following would be the standard deviation?
6
Another name for the Empirical Rule is which of the following?
68-95-99.7 Rule
If there are 40 people in a study and 28 of them have blue eyes, what percent of the people in the study has blue eyes?
70%
If the correlation coefficient has been calculated to be 0.87, what would be the value of the coefficient of determination?
75.69%
Which of the following statements is NOT true?
A strong correlation between two variables indicates a cause/effect relationship between the variables.
Last year it was determined that about 90% of the drivers in a given city wore their seat belts. It is believed that this percentage has decreased. Data is collected to test this conjecture. Which of the following would be the appropriate hypotheses for this test?
H0 : p = .90 Ha : p < .90
A filling machine should be putting 12 ounces of soda into a can. If the machine is out of adjustment, it may be overfilling or underfilling the cans, and either of those is not acceptable. Data will be gathered to check the machine's adjustment. What would be the hypotheses for this test?
H0 : μ = 12 Ha : μ ≠ 12
When two events A and B are independent, what does this mean?
If A occurs, it has no effect on the likelihood of B occurring.
Which of the following is NOT true of the correlation coefficient (r)?
If r = -.9, this indicates a weak linear relationship between the two variables.
When is it correct to use the formula to find the standard deviation for a given population?
It can be used only for a Binomial population.
Which of the following is NOT true of the null hypothesis H0 ?
It contains the challenge or research question to be tested.
In an hypothesis test, which of the following is true of a sample (test) statistic whose value is far away from the value in the null hypothesis H0 ?
It supports the research hypothesis Ha.
Sampling distributions consist of values gathered from lots and lots of samples. What must be true of those samples?
all samples must be the same size
The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics: Anesthetic C appears dangerous. The National Halothane Study is which of the following?
an observational study
For what kinds of distributions does the Empirical Rule apply?
any bell-shaped distribution
A p̂ sampling distribution will be normal under what circumstances?
both np and nq are at least 5
To see if a Binomial distribution is normal in shape, which of the following must be true?
both np and nq must be 5 or more
Suppose P(A) = .4 and P(B) = .5. What is P(A ∩ B)?
can't be determined
At a local community college, five mathematics classes are randomly selected and all of the students from each selected class are interviewed. What sampling technique is used?
cluster sampling
To estimate the average gas mileage for a certain model of SUV, a random sample of 30 of these SUV's is selected and driven. The mean gas mileage in the sample was 27.3 mpg. Records provided by the vehicle manufacturer indicate that the standard deviation for the gas mileage of these vehicles is 3.6 mpg. To use this information to construct a 90% confidence interval for the average gas mileage of all SUV's of this type, which of the following formulas would be used?
x̅ ± 1.645 (σx̅)
To estimate the average weight of an adult passenger on a large international flight, a random sample of 30 adult passengers is selected. The mean weight in the sample is 178 lbs and the standard deviation in the sample was 8.3 lbs. To use this information to construct a 90% confidence interval for the average weight of all adult passengers on this flight, which of the following formulas would be used?
x̅ ± 1.699 (σx̅)
What is the probability that a sample mean (x̅) will perfectly match the mean of the population (μ)?
zero
