busi 2305 chap 9 smartbook
True or false: A Type I error occurs if we do NOT reject the null hypothesis when it is actually false.
False
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.
In hypothesis testing, two correct decisions are possible:
Do not reject the null hypothesis when it is true. Reject the null hypothesis when it is false.
The two equivalent methods to solve a hypothesis test are the
critical value approach. p-value approach.
A hypothesis test can be -tailed or -tailed
one two
If we reject the null hypothesis when it is actually false we have committed...
no error.
For an alternative hypothesis of HA: μ > μ0, we might possibly reject the null hypothesis if
the population mean is greater than μ0.
The critical value of a hypothesis test is
the value that separates the rejection region from the non-rejection region.
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
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.
An auditor for a small business wants to determine whether the mean value of all accounts receivable is less than $550. She takes a sample of 40 and computes the sample mean and the sample standard deviation. The null and alternative hypotheses for this test are
H0: μ ≥ 550 and HA: μ < 550
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
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
If the underlying population is not normally distributed, we need the sample size to be at least
30 or thirty
The p-value approach to hypothesis testing has steps.
4 or four
The null hypothesis is specified by using one of the following signs:
=, ≤, or ≥
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.
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
Which of the following is NOT a step in the p-value approach to hypothesis testing?
Graph the distribution of the sample data
Which of the following are correctly configured one-tailed tests?
H0: p > p0 HA: p < p0 H0: μ < μ0 HA: μ > μ0 H0: p < p0 HA: p > p0 H0: μ > μ0 HA: μ < μ0
H0 HA
Null hypothesis Alternative hypothesis
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
True or false: The optimal values of Type I and Type II errors require a compromise in balancing the costs of each type of error.
True
Rejecting the null hypothesis when the null hypothesis is true.
Type I error
We define α as the the probability of making a Type I error.
allowed or allowable
α is the probability of a Type I error.
allowed or allowable
The conclusions of a hypothesis test that are drawn from the p-value approach versus the critical value approach are
always the same.
Hypothesis testing is analogous to a criminal court of law where someone is until proven
innocent guilty
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, report, or communicate
Not rejecting a true null hypothesis.
Correct decision
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
Typically, the decision regarding the optimal level of Type I and Type II errors is made by the
management
The p-value is calculated assuming the
null hypothesis is true.
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.
Rejecting a false null hypothesis.
Correct decision
The alternative hypothesis for a one-sided test looks like:
HA: μ < μ0
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 p-value is referred to as the probability of making a Type I error.
observed
When performing a hypothesis test on μ, the p-value is defined as the
observed probability of making a Type I error.
A one-tailed test involves a null hypothesis that can only be rejected on side of the hypothesized value.
one
The critical value approach specifies a region of values, called the ______. If the test statistic falls into this region, we reject the ______.
rejection region, null hypothesis
When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a
right-tailed test.
In inferential statistics, we use information to make inferences about an unknown parameter
sample population
For a hypothesis test of μ when σ is known, the value of the test statistic is calculated as
z = x−μ0/σ/n√
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
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 -2.50 and the critical value at the 5% level of significance is -z0.05 = -1.645, then the correct conclusion is:
Reject H0 and conclude that the population mean appears to be less than 10 at the 5% significance level.
Which of the following types of hypothesis tests may be performed?
Right-tailed, left-tailed, and two-tailed tests
The significance level is the probability of making
a Type I error.
For a given sample size n, α can only be reduced...
at the expense of increasing β.
An important final conclusion to a statistical test is to...
clearly interpret the results in terms of the initial claim
We reject H0 if the p-value is alpha
less than
Which of the following is true?
α = the probability of committing a Type I error; β = the probability of committing a Type II error.
We can generally reduce both Type I and Type II errors simultaneously by...
increasing the sample size.
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.
Which of the following are correctly configured two-tailed tests?
H0: μ = μ0 HA: μ ≠ μ0 H0: p = p0 HA: p ≠ p0
In general, we follow three steps when formulating the competing hypotheses. Place these steps in the correct sequence
Identify the relevant population parameter of interest. Determine whether it is a one or two tailed test. Include some form of equality sign in the null hypothesis and use the alternative hypothesis
In order to implement an hypothesis test, it is essential that XX is distributed
normally
Hypothesis testing enables us to determine if the collected ______ data is inconsistent with what is stated in the null hypothesis.
sample
The only way we can reduce both Type I and Type II errors is by increasing
sample size
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 statistics and its p-value state the conclusion and interpret results
If the population standard deviation is unknown, it can be estimated by using ______.
s
We always use evidence and the chosen significance level α to conduct hypothesis tests.
sample
For a hypothesis test on μ when the value of σ is unknown, the value of the test statistic is calculated as ______, provided that we sample from a normal population.
tdf = x−μ0s/√nx-μ0s/n
By reducing the likelihood of a Type I error, we the likelihood of a Type II error,
increase or raise
The test statistic when the population standard deviation is know is z = x−μ0σ/√nx-μ0σ/n. This formula is valid only if XX follows a distribution
normal
The approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand.
critical value
If the value of the test statistic falls in the rejection region, then the p-value must be
less than α.
The alternative hypothesis typically _____
contests the status quo and may suggest a corrective action if true.
The optimal choice of α and β depends on the relative of these two types of errors.
cost
There are two equivalent methods to test a hypothesis: the p-value approach and the approach.
critical value
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
A Type I error occurs when we the null hypothesis when it is true
reject
If the chosen significance level is α = 0.05, then there is a 5% chance of
rejecting a true null hypothesis.