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Terms in this set (46)
continuous
A random variable that assume any value from an interval (or collection of intervals) is called
The number of arrivals to a bank in a two hour period
Which of the following random variables is not continuous (is discrete)?
probability density function
The function that defines the probability distribution of a continuous random variable is a
all of the above
A continuous random variable with the uniform distribution on an interval [a,b] satisfies the following:
Both tails of a normal curve (normal density function) are asymptotical in the sense that they approach the horizontal axis and touch it.
Which of the following is not a characteristic of normal distributions?
the standard normal distribution (the z distribution)
A normal distribution with a mean of 0 and a standard deviation of 1 is called
z = (x - μ)/σ
Any normal variable with mean μ and standard deviation σ can be converted into the standard normal variable by the following transformation
0.9544
The probability that a normal random variable with mean μ and standard deviation σ falls in between
μ - 2σ and μ + 2σ is
population based upon information contained in the sample
The main purpose of Inferential Statistics is to provide information about the
numerical characteristics of a population
Parameters are
numerical characteristics of a sample
Statistics are
data from the sample is used to estimate unknown population parameters
The main idea of estimation is that
a point estimate of the corresponding unknown population parameter (μ, σ, and p)
The calculated value of a sample statistic (such as sample mean , sample standard deviation s, or sample proportion ) is
a point estimator
The sample statistic (such as sample mean , sample standard deviation s, or sample proportion ) that provides the point estimate of the corresponding population parameter (μ, σ, and p) is called
can be smaller, larger, or equal to the corresponding unknown population parameter
Since the sample size is always smaller than the population size, the calculated value of a sample statistic
probability distribution of the sample mean
The sampling distribution of is the
the expected value E(x ̅ )=μ and standard deviation σ_x ̅ =σ/√n
If a population (regarded as infinite) has mean µ and standard deviation σ, the mean x ̅ in a random sample of n observations has
normal with the expected value 75 and standard deviation 1.6
Historically, students who take BUAD 2060 have a mean score of 75 and a standard deviation of 8. The score distribution can be assumed normal. A random sample of 25 BUAD 2060 students is selected. What can be said about the distribution of their average score?
the sampling distribution of the sample proportion p ̅
The probability distribution of all possible values of p ̅ is called
the expected value E(p ̅ )=p and standard deviation σ_p ̅ =√(p(1-p)/n)
If the population proportion (for infinite population) is p, the proportion p ̅ in a sample of n observations has
0.35 and 0.0954
Historically, 35 percent of students who take BUAD 2060 earned at least grade B. A random sample of 25 BUAD 2060 students is selected. The expected value and the standard deviation of the proportion of those who will earn at least B are
a normal distribution
According to the central limit theorem, as the sample size becomes larger, the sampling distributions of x ̅ and p ̅ become closer to
n ≥ 30
For most applications with a continuous population, the sampling distribution of the sample mean x ̅ is approximately normal if the sample size satisfies
np ≥ 5 and n(1-p) ≥ 5
Which conditions must be met to assume the normality of the sampling distribution of the sample proportion p ̅?
interval estimate
An estimate of a population parameter that provides an interval of values believed to contain this parameter is known as the
margin of error
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
[Point estimate - Margin of errors, Point estimate + Margin of error]
The most typical form of the confidence interval for a population parameter is
the confidence level
The ability of an interval estimate to contain the population parameter is described by
If the sample size is greater, the confidence interval is narrower
For a given confidence level and population or sample standard deviation, which of the following is true in the interval estimation of the population mean?
If the confidence level is greater, the confidence interval is wider
For a given sample size and population or sample standard deviation, which of the following is true in the interval estimation of the population mean?
the normal distribution
For the interval estimation of the population mean , when the population standard deviation is known and the sample is sufficiently large, the proper distribution to use is
normal distribution
In order to use the normal distribution for interval estimation of the population mean , when the population standard deviation is known and the sample is small, the population must have
t distribution
Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which of the following distributions is used in developing an interval estimate for the population mean?
becomes smaller
As the number of degrees of freedom of the t distribution increases, the difference between the t distribution and the standard normal distribution
t distribution with 24 degrees of freedom
From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of , the proper distribution to use is the
Increase the sample size
After finding a confidence interval for the population mean, the user believes the result is meaningless because the interval is too wide. Which one of the following is the best recommendation?
hypothesis
An assumption made about the value of a population parameter is called a
do not reject, reject
If the probability of making type II error is not examined, then the conclusion in all hypothesis testing is to______the null hypothesis, or ______the null hypothesis.
Type I
What type of error occurs if you reject H0 when it is actually true?
a false null hypothesis is not rejected
A Type II error is committed when
maximum allowable probability of making Type I error
The level of significance is the
at least as small as that provided by the sample
For a lower tail test, the p-value is the probability of obtaining a value of the test statistic
p-value
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
the level of significance
Which of the following does not need to be known in order to compute the p-value?
will also not be rejected at the 1% level
If a null hypothesis is not rejected at the 5% level of significance, it
must be rejected
A two-tailed test is performed at the 5% level of significance. The p-value is determined to be 0.04. The null hypothesis
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Verified questions
STATISTICS
Suppose Compositor A is preparing a manuscript to be published. Assume that she makes X errors per page, where X has a Poisson pdf, with $\lambda=2$. A second compositor, B, is also working on the book. He makes Y errors on a page, where Y is Poisson with $\lambda=3 .$ Assume that Compositor A prepares the first one hundred pages of the text and Compositor B, the last one hundred pages. After the book is completed, reviewers (with too much time on their hands!) find that the text contains a total of five hundred twenty errors. Write a formula for the exact probability that fewer than half of the errors are due to Compositor A.
STATISTICS
Consider the following hypothesis test: $$ \begin{array} { l } { H _ { 0 } : \mu = 15 } \\ { H _ { \mathrm { a } } : \mu \neq 15 } \end{array} $$ A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. a. Compute the value of the test statistic. b. What is the p-value? c. At α = .05, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion?
QUESTION
Your family has an iPod filled with music. It has many thousands of songs. You figure that roughly 60% of the songs are music you like, 25% of the music is annoying songs from your little sister, and the rest is stuff from the 80s that only your parents still think is cool. Driving across town, your Mom puts the iPod on shuffle and you all listen to whatever randomness produces. What is the probability that the first song is not one of your songs?
QUESTION
Identify the experimental units, the explanatory and response variables, and the treatments. A maker of fabric for clothing is setting up a new line to "finish" the raw fabric. The line will use either metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing-cycle time of either 30 or 40 minutes; and a temperature of either $$ 150^{\circ} $$ or $$ 175^{\circ}C. $$ An experiment will compare all combinations of these choices. Three specimens of fabric will be subjected to each treatment and scored for quality.