STATS Exam 3
If an interval estimate is said to be constructed at the 95% confidence level, the significance level is ___.
0.05
Consider the following hypothesis test: Ho: μ= 60 H1: μ≠ 60 A sample of 16 observations has a sample mean of 61.5. The population standard deviation is known to be 4. Based on this information, it was found that the test statistic is equal to 1.5. Find the p-value for the test.
0.1336
Area under t distribution curve equals ____.
1
Confidence level equation
1-alpha
significance level equation
1-confidence level
According to a Lawyers.com survey, only 30% of adult Americans had a will. Suppose a recent survey of 250 adult Americans found 100 adults with wills. You are interested to determine whether the proportion of adult Americans who have a will differs from the reported based on your data. Compute the value of the test statistic for this test.
3.4503
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of Type I error if the new blood test is used?
5%
If alpha = 0.1, confidence level is ____.
90%
What does a confidence level of 90% mean?
90% of intervals contain mean, 10% d not
What is an estimate?
a particular value of the estimator obtained from the sample
What does an interval estimate provide?
a range of value that best describes the population parameter of interest
A point estimator provides _____.
a single value or a point
What is an estimator?
a statistic used to estimate a population parameter
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease H1: A person has disease In this example, when the Type I error is commited, we conclude that...
a truly healthy person has a disease
critical z score
a value of z which corresponds to the area of a/2 on the right in the standard normal distribution
The hypothesis statement 𝐻0:𝜇≠5 is an example of
alternative hypothesis in a two-tail test
What is the confidence interval for the proportion?
an interval estimate around a sample proportion that provides us with a range of value within which the true population proportion is expected to lie
What is a confidence interval for the mean?
an interval estimate around the sample mean that provides us with a range which might contain the true population mean
Which of the following represents an appropriate NULL hypothesis in the lower tail test? a. H0:μ<0 b. 𝐻0:𝜇≥0 c. 𝐻0:𝜇≤0 d. 𝐻0:𝜇>0
b. 𝐻0:𝜇≥0
When the sample size is less than 30 and σ is known, the population must ...
be normally distributed to calculate the confidence interval
As the number of degrees of freedom for the t distribution increases, the difference between the t distribution and the standard normal distribution ______.
becomes smaller
The graph of t-distribution is ____ shaped.
bell (symmetrical)
As we increase the confidence level, the range will be _____.
bigger
Proportion data follow the ________ distribution, which can be approximated by the ________ distribution under the following conditions: nπ ≥ 5 and n(1 - π) ≥ 5.
binomial, normal
The alternative hypothesis typically...
contest the status quo
As the sample size n increases, the margin of error ____.
decreases
the shape of a t distribution depends on....
degrees of freedom
When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called _____.
estimate
When the population standard deviation is unknown, substitute _____ in its place.
sample standard deviation
In the point estimation, data from the ____ is used to estimate the _____.
sample, population parameter
The variable a is known as the _____.
significance level
As the number of degrees of freedom for a t distribution increases, the shape of the t-distribution becomes...
similar to the normal distribution
As we decrease the confidence level, the range will be ______.
smaller
standard error of the mean equation
standard deviation / square root of sample size
When conducting a hypothesis test for the population mean when σ is known and the sample size is 30 or more, the distribution we use for computing the critical value and the p-value is...
standard normal distribution
Confidence level and length of the confidence interval have a ____ relationship.
strictly positive
When the population standard deviation is unknown us the ____ score.
t
In hypothesis testing, if the null hypothesis is rejected,...
the alternative hypothesis is true
What is the margin of error?
the amount added and subtracted to the point estimate to form the confidence interval
T/F When testing for the population mean when the population standard deviation is known (and a sample size is greater than 30), a standard normal distribution is used to calculate the critical value and the p-value.
true
T/F When the population standard deviation is unknown, we substitute the sample standard deviation in its place to calculate a confidence interval for the mean.
true
T/F When we use the z-distribution to calculate a confidence interval, we need to assume that the population of interest follows the normal probability distribution if the sample size is small (less than 30 observations).
true
The error of rejecting a true null hypothesis is...
type I error
What types of tests about the population parameter may be performed?
upper tail, lower tail, two tail tests
If the population standard deviation is larger, the interval is _____.
wider
degrees of freedom
n-1
As the confidence level decreases, the confidence interval becomes...
narrower
As the sample size n increases, the confidence interval becomes...
narrower
Decreasing margin of error results in a _____ confidence interval.
narrower
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
A Type I error
t distribution
A distribution specified by degrees of freedom used to model test statistics for the sample mean, differences between sample means, etc. where IT (' s) is (are) unknown
In order to construct the interval estimate of the population mean µ when σ is known and the sample is very small, the population data must be _____.
normally distributed
X_bar is the point estimator of _____.
population mean
p_bar is the point estimator of _____.
population proportion
The sample standard deviation is the point estimator of the ___
population standard deviation
s is the point estimator of ______.
population standard deviation (s)
Increasing the sample size while keeping the confidence level constant will _____ the margin of error.
reduce
T/F We cannot establish a claim if the null hypothesis is not rejected.
true
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighted to determine whether overfilling or underfilling is occurring. If the sample data led to a conclusion of underfilling or overfilling, the production line would be shut down and adjusted to obtain a proper filling. The correct hypothesis statement for this test would be...
H0 : μ = 32 ; H1 : μ ≠ 32
What is the most typical form of a calculated confidence interval?
Point estimate +_ Margin of error
Whenever estimating the confidence interval for the population proportion, what is required?
The sample size and the population proportion should be such that np≥ 5 and n(1 - p) ≥ 5.
T/F The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean.
True
T/F All else being equal, a 90% confidence interval will be wider than a 95% confidence interval.
false
T/F For an upper-tail hypothesis test, if the z test statistic exceeds the critical value, we do not reject the null hypothesis.
false
T/F Given that a 95% confidence interval is [6.5, 12.5], we can state that there is a 95% probability that the true population mean is between 6.5 and 12.5.
false
T/F If the hypothesis test is to be used in an attempt to prove a particular point of view, you would assign the null hypothesis to establish the point of view you favor.
false
T/F If we fail to reject H0 when, in fact, it is not true, we commit a Type I error.
false
T/F On the basis of sample information, we can either "accept the null hypothesis" or "reject the null hypothesis".
false
T/F The confidence interval for the the mean is symmetrical around the population mean.
false
T/F The margin of error can be reduced by reducing the size of the sample.
false
T/F The p-value for a test is the probability that the null hypothesis is true.
false
T/F When testing for the population mean when σ is known and a sample size is greater than 30, the population must be normally distributed in order for the conclusions to be reliable.
false
T/F When the p-value is greater than the significance level, the conclusion for the hypothesis test is to reject the null hypothesis.
false
The t-distribution is ____ and ____ than the standard normal distribution.
flatter, wider
Suppose that you are working on an upper tail test. As the test statistic becomes larger, the p-value...
gets smaller.
Do interval estimates always contain the true mean?
given the fixed length of an interval, there are many possible intervals depending on the value of x
The critical score for the t-distribution is _____ than the critical z-score for the same confidence level.
greater
In a standard normal distribution, the probability associated with the interval -1 to -2 is _______ the probability associated with the interval 1.5 to 2.5.
larger than
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
The center of a normal curve is the ________ of the distribution.
mean
confidence level
the estimated probability that a population parameter lies within a given confidence interval
Lower Confidence Limit
the lower bound of the confidence interval
In hypothesis testing, the tentative assumption about the population parameter is...
the null hypothesis
UCL and LCL describe...
the range where we have some degree of confidence that the actual population mean lies
For the interval estimation of µ when σ is known and the sample is large, the proper distribution to use is _____.
the standard normal distribution
When s is used to estimate the confidence interval for the mean, the margin of error is computed by using...
the t distribution
When s is used to estimate σ, the margin of error is computed by using _____.
the t distribution
For the confidence interval of the mean when the population standard deviation is unknown and the sample is large, the proper distribution to use is...
the t distribution with n-1 degrees of freedom
Upper Confidence Limit (UCL)
the upper bound on the confidence interval
The confidence intervals for the population proportion are generally based on...
the z distribution
The confidence intervals for the population proportion are generally based on ____.
the z-distribution
T/F For a two-tail hypothesis test, if the absolute value of the z test statistic exceeds the critical value (i.e. exceeds the absolute value of the critical z), we reject the null hypothesis.
true
T/F For an upper-tail test, the p-value is computed as the probability of obtaining a z test statistic at least as large as the one calculated based on the sample.
true
T/F In a one-tail test, the rejection region is located under one tail (upper or lower) of the corresponding sampling distribution, while in a two-tail test this region is located under both tails.
true
T/F In the hypothesis tests, the null hypothesis is believed to be true unless there is overwhelming evidence to the contrary.
true
T/F The definition of a 90% confidence interval is that we expect that close to 90% of a large number of sample means drawn from a population will produce confidence intervals that include that population's mean.
true
T/F The hypothesis statement H: μ < 60 is an example of an alternative hypothesis in a one-tail test
true
T/F The point estimate of the population mean will always be found within the limits of the confidence interval for the mean.
true
T/F There is no guarantee that every confidence interval constructed for the mean will include the population mean.
true
Consider the following hypothesis test: Ho: 𝜇 ≥ 0.3 H1: 𝜇 < 0.3 The null hypothesis will be rejected at the significance level α if
𝑧𝑝 < -𝑧𝛼