BSTAT Ch.9
The p-value is the likelihood of obtaining a sample mean that is at least as _______ as the one derived from the given sample, under the assumption that the null hypothesis is true as an equality.
Extreme
The p-value is referred to as ________ the probability of making a Type I error.
Observed
The normal distribution approximation for a binomial distribution is valid when
np ≥ 5 and n(1 - p) ≥ 5
The hypothesis testing procedure enables us to make one of __________ decisions.
two
We always use ________ evidence and the chosen significance level α to conduct hypothesis tests
sample
A binomial distribution can be approximated by a ______________ distribution for large sample sizes
Normal
The test statistic when the population standard deviation is know is z = /x−μ0σ/√nx-μ0σ/n. This formula is valid only if /X follows a ______ distribution
Normal
True or false: Consider the following competing hypotheses: H0: μ = 150 versus HA: μ ≠ 150. If a 95% confidence interval is [100, 200], then we cannot reject the null hypothesis at the 5% significance level
True
Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 5% significance level, the critical value(s) for a two-tailed test is (are):
-z0.025 and z0.025
Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a left-tailed test is (are):
-z0.10
As a point estimate of the population proportion, we calculate _______
/P
Which of the following statements is NOT correct concerning the p-value and critical value approaches to hypothesis testing?
Both approaches use the same decision rule concerning when to reject H0
Suppose the competing hypotheses for a test are H0: μ = 10 versus HA: μ ≠ 10. If the value of the test statistic is 1.87 and the critical values at the 5% level of significance are -z0.025 = -1.96 and z0.025 = 1.96, then the correct conclusion is:
Do not reject H0 and conclude that the population mean does not appear to differ from 10 at the 5% significance level.
True or false: A Type I error occurs if we do NOT reject the null hypothesis when it is actually false.
False
True or false: In the critical value approach, if the value of the test statistic does not fall within the rejection region, then we reject the null hypothesis
False
The p-value approach to hypothesis testing has ______ steps.
Four
Specify the competing hypotheses in order to determine whether the population proportion differs from 0.60
H0: p = 0.60 versus HA: p ≠ 0.60
Specify the competing hypotheses that would be used in order to determine whether the population proportion is greater than 0.35
H0: p ≤ 0.35 and HA: p > 0.35
An auditor for a small business wants to test the assumption that the mean value of all accounts receivable differs from $550. She takes a sample of 40 accounts and calculates the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are
H0: μ = $550 and HA: μ ≠ $550
The null hypothesis for a two-sided test for a population mean would be denoted as
H0: μ = μ0
H0: HA:
Null Hypothesis Alternative Hypothesis
The hypothesis denoted by H0 is the __________ hypothesis and the hypothesis denoted by HA is the ___________ hypothesis.
Null and alternative
The basic principle of hypothesis testing is to first assume that the ______ hypothesis is true and then determine if the sample data _______ this assumption.
Null, contradict
The _______ level of a hypothesis test is defined as 100α%.
Significance
Put the following steps in the p-value approach to hypothesis testing in the correct order
Specify the null and alternative hypotheses; Specify the significance level; Calculate the value of the test statistic and its p-value; State the conclusion and interpret results
Rejecting the null hypothesis when the null hypothesis is true
Type I error
The conclusions of a hypothesis test that are drawn from the p-value approach versus the critical value approach are
always the same
An important final conclusion to a statistical test is to...
clearly interpret the results in terms of the initial claim
The optimal choice of α and β depends on the relative______ of these two types of errors
cost
Consider the following competing hypotheses: H0: μ = 10 versus HA: μ ≠ 10. If a 95% confidence interval is [8.25, 11.55], then at the 5% significance level we
do not reject the null hypothesis and conclude that the population mean does not significantly differ from 10
When performing a hypothesis test on μ, the p-value is defined as the
observed probability of making a Type I error
E(/P)=
p
When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a
right-tailed test
If the population standard deviation is unknown, it can be estimated by using
s
We would conduct a hypothesis test to determine whether or not
sample evidence contradicts H0.
When performing a hypothesis test on μ when the value of σ is unknown, the test statistic is computed as x−μ0s/√nx-μ0s/n and it follows the
tdf distribution with (n - 1) degrees of freedom.
When performing a hypothesis test on μ when σ is known, H0 can never be rejected if
z ≥ 0 for a left-tailed test.
Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 5% significance level, the critical value(s) for a right-tailed test is (are):
z0.05
Which one of the following is NOT a step we use when formulating the null and alternative hypotheses?
Calculate the value of the sample statistic.
Not rejecting a true null hypothesis
Correct decision
By reducing the likelihood of a Type I error, we _______ the likelihood of a Type II error,
Increase
Hypothesis testing is analogous to a criminal court of law where someone is _____ until proven ________
Innocent; guilty
A one-tailed test involves a null hypothesis that can only be rejected on ______ side of the hypothesized value
One
Formulating the competing hypothesis
1.) Identify the relevant population parameter of interest 2.) Determine whether it is a one-two tailed test 3.) Include some form of the equalitiy sign in the null hypothesis and use the alternative hypothesis to establish a claim
In a hypothesis test, μ0 and p0 are hypothesized values of the ______ mean and the ______ proportion, respectively
Population; Population
The critical value approach specifies a region of values, called the ______. If the test statistic falls into this region, we reject the ______
Rejection; null hypothesis
Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are
Categorical or quantitive
The ________________ approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand
Critical Value
It is not sufficient to end the analysis with a conclusion that you reject the null hypothesis or you do not reject the null hypothesis. You must _______ the results
Interpret
Typically, the decision regarding the optimal level of Type I and Type II errors is made by the
Management
If we reject the null hypothesis when it is actually false we have committed...
No error
In most applications, we require some form of the equality sign in the _______ hypothesis.
Null
A Type I error occurs when we _________ the null hypothesis when it is true
reject
Consider the following competing hypotheses: H0: μ = 10 versus HA: μ ≠ 10. If a 95% confidence interval is [15, 20], then at the 5% significance level we
reject the null hypothesis and conclude that the population mean appears to differ from 10
The critical value of a hypothesis test is
the value that separates the rejection region from the non-rejection region
Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus HA: μ > 10. If the value of the test statistic is 1.90 and the critical value at the 1% level of significance is z0.01 = 2.33, then the correct conclusion is:
Do not reject H0 and conclude that the population mean does not appear to be greater than 10 at the 1% significance level.
The p-value approach to hypothesis testing has ______ steps
four
In hypothesis testing, the standard error of the sample proportion /P is computed as
po(1−po)/n sqrt.
For a given sample size n, α can only be reduced...
at the expense of increasing β
If the value of the test statistic falls in the rejection region, then the p-value must be
less than a
