Chapter 9
Given the following hypotheses: H0: π ≤ .25 vs. H1: π > .25, zcalc = 2.30. The p-value is
0.0107
A 95% confidence interval could be used to conduct a two-tailed hypothesis test when alpha is
0.05
For a two-tailed test with zcalc = -1.80, the resulting p-value is
0.0719
For a right-tailed test with zcalc = 1.45, the p-value is
0.0735
For a two-tailed test of a proportion, zcalc = 1.30. The p-value is
0.1936
For a two-tailed test with zcalc = 0.78, the resulting p-value is
0.4354
In hypothesis testing, 2 correct decisions are possible:
1. Rejecting the null hypothesis when the null hypothesis is false. 2. Not rejecting the null hypothesis when it is true.
Which variables below would express proportion data?
1. The number of customers who agree that the new product price is acceptable. 2. The number of employees who reported an accident last month.
We would not reject the null hypothesis when the p-value is
1. greater than the level of significance. 2. close to 1.0
A statistical hypothesis test requires that we
1. identify the population parameter of interest. 2. determine whether it is a one- or a two-tailed test.
The p-value method for testing hypotheses is often preferred by statisticians because
1. it is more flexible than the critical value method. 2. it does not involve a test statistic.
Steps in order of hypothesis testing
1. state hypothesis 2. specify decision rule 3. collect data 4. make decision 5. take action
The critical z value is
1. the z value associated with level of significance. 2. the z value that separates the rejection region from the non-rejection region.
All business managers need a basic understanding of hypothesis testing because
1. they often interact with specialists, 2. they are required to read and understand technical reports, 3. they must make decisions based on statistical evidence.
The critical value of z for a right-tailed test with α = .10 is
1.28
When testing a hypothesis about a proportion and π0 = .25, then n ≥ _________ in order to assume normality. (Round the value to the nearest whole number.)
40
To find the two-tailed p-value for a test statistic tcalc using Excel use the following formula:
=t.dist.2t(tcalc, df)
A hypothesis is also known as an
Assumption or theory
True or false: A Type I error is when we FAIL to reject the null hypothesis when it is actually false.
False
True or false: A null hypothesis can be proved true.
False
An auditor for a small business wants to test the assumption that the mean value of all accounts receivable is greater than or equal to $550 by taking a sample of 40 and computing the sample mean. The auditor will reject the null only if the sample mean is clearly less than $550. The null and alternative hypotheses for this test are
H0: μ ≥ $550 and H1: μ < $550
A business believes their supplier's delivery times have increased over the past few months. To test this belief they would use which alternative hypothesis?
H1: μ > μ0
A service company would like to know if the proportion of customers satisfied with their service has changed since the last time they surveyed their customers. Their alternative hypothesis would be
H1: π ≠ π0
Which of the following are common values for α?
0.01, 0.05, 0.1
The power of a test is measured by
1 - β
In hypothesis testing, there are 2 possible incorrect decisions:
1. Not rejecting the null hypothesis when it is false. 2. Rejecting the null hypothesis when it is true.
The critical value of z for a two-tailed test with α = .01 is
2.576
Given the following set of hypotheses: H0: No illegal steroid use H1: Illegal steroid use, which statement describes the consequence of a Type I error?
An athlete is banned from competing when he or she did not use illegal steroids.
For the following hypotheses and sample result choose the correct conclusion: H0: μ = 67 vs. H1: μ ≠ 67. z critical = ± 1.645 and zcalc = 1.56.
Fail to reject the null hypothesis and conclude that there is not significant evidence to state μ ≠ 67.
Match the hypotheses with the correct label. Instructions
H0: μ0 = 5 - two H1: μ0 ≠ 5 - two H0: μ0 ≥ 5 - left H1: μ0 < 5 - left H0: π0 ≤ .34 - right H1: π0 > .34 - right
A researcher for a store chain wants to test the assumption that the mean proportion of all people who shop in the store(s) who try the samples offered is 0.15. She thinks that the proportion is actually higher than 0.15. The null and alternative hypotheses for this test are
H0: π ≤ 0.15 and H1: π > 0.15
Suppose a hypothesis test resulted in a p-value = .0456. Match the significance level to the correct conclusion.
Reject H0 - 0.1, 0.05 fail to reject H0 - 0.01
A right-tailed hypothesis test for a mean resulted in tcalc = 2.23 with df = 16. If α = .05 the correct conclusion would be
Reject the null because the p-value < .05.
For the following hypotheses and sample result choose the correct conclusion: H0: μ ≤ 25 vs. H1: μ > 25. z critical = +1.96 and zcalc = 2.09.
Reject the null hypothesis and conclude that μ > 25.
Which of the following are NOT options in Excel for calculating a p-value from a t distribution?
T.DIST.LT
Given the following set of hypotheses: H0: Defendant is not guilty H1: Defendant is guilty, which statement describes the consequence of a Type II error?
The defendant is not convicted of the crime but was guilty.
A manager tested the following hypotheses about the average days until an invoice was paid: H0: μ ≤ 15 vs.H1: μ > 15. The resulting p-value = .024. The level of significance used was .05. Which of the following is a valid conclusion?
The manager would reject the null hypothesis and conclude that the average number of days to pay an invoice was greater than 15.
A test statistic is
a standardized score of a sample statistic.
True or false: All statistically significant result have practical importance.
false
For a given sample size, reducing α results in an
increase in β.
True or false: A null hypothesis corresponds to the status quo or current state.
True
True or false: All business managers need a basic understanding of hypothesis testing.
True
True or false: An alternative hypothesis should never have an equal sign.
True
True or false: If a critical value is set at 1.645 for a right-tailed test, a calculated test statistic of 1.82 would lead to the null hypothesis being rejected.
True
The significance level is the probability of making a
Type I error (α)
An example of the relevance of making inferences using a population variance is
a coffee vending machine wanting to put a certain amount of beverage in a cup, without being too little or spilling over.
If a 90% confidence interval for a store's customer accounts is computed as $850 ± 70, then the null hypothesis that μ = $750 would
be rejected at α = .10.
The parameter value in the null hypothesis is called a _______ and the value does not come from a _____
benchmark, sample
When testing a population proportion, if either nπ0 or n(1-π0) are less than 10, one must calculate a p-value using the _________ distribution.
binomial
Statistical inference regarding a population variance is based on the
chi-square distribution.
A decision rule states what the value of the test statistic must be in order to reject the null hypothesis. This value is called the _________ value
critical
Hypothesis testing uses sample __________ to test assumptions
data
Even though repeated hypothesis tests could result in no strong conflicts between the observed data and the null hypothesis, one would still not state the null has been proved, one would state that they would ________ __________ ___________ the null hypothesis
fail to reject
True or false: Smaller values of α make it easier to reject the null.
false
True or false: Using a z score instead of t statistic to test a mean when sigma is unknown will increase Type II error.
false
__________ testing is used by business managers to guide decision making.
hypothesis
It is possible to see a statistically significant change in a population parameter even though the difference does not have practical implications
if a very large sample was taken which can illuminate very small changes in a population mean.
We can generally reduce the probability of Type II errors by
increasing the sample size.
The conclusion drawn from the p-value approach or the critical value approach
is the same
The critical value stated in the decision rule is determined by
level of significance
Alpha (α) is known as the significance _____ and defines the rejection _____ in the tailed test
level, region
The critical value is determined by the chosen ___________ of ________
level, significance
Increasing the value of alpha in a hypothesis test will
make it less difficult to reject the null hypothesis,
When finding a p-value for a two-tailed test, it is important to __________ the tail area associated with zcalc by __________ because the α area is split between the upper and lower tails.
multiply, two
A Type II error is made when we fail to reject the __________ hypothesis when it is actually false.
null
The normal distribution approximation for a binomial distribution is valid when
nπ0 ≥ 10 and n(1-π0) ≥ 10
The __________ method is often preferred to the critical value method because it is a direct measure of the likelihood of observing the sample with the null hypothesis is true.
p-value
In using Excel to calculate p-values from a t distribution, we can select Formulas > Insert Function > T.DIST.2T. This command returns the
p-value associated with the relevant t-value for a two-tailed test.
The mean of the sampling distribution of p is the ______ proportion
population
The chi square distribution is
right
The t statistic assumes that the population is normally distributed. However, t-test results are considered fairly ________ to non-normality as long as there are no _________
robust, outliers
the ________ the p-value, the more inclined we are to reject the null hypothesis.
smaller
The test statistic used for testing μ when the population mean, σ, is unknown is
tcalc =x−μ0s/n√
A quality control engineer would like to test if the average time of use for AAA batteries is equal to 8.5 hours. She does not know the population standard deviation. If a sample of 32 batteries is tested, the test statistic would be calculated as
tcalc= x bar - 8.5 / (s/square root 32), with df=31
The difference between the sample statistic and the null hypothesis value is measured by a
test statistic.
The p-value is calculated assuming the
the null hypothesis is true.
The power of a test is defined as
the probability of rejecting the null hypothesis when the null hypothesis is false.
For an alternative hypothesis of H1: μ > μ0, we would reject the null hypothesis only when
the sample mean is greater than μ0.
There is little difference between critical values of t and z when ___.
the sample size is large (n > 30)
True or false: A proportion can be expressed as percentage but not all percentages can be expressed as a proportion.
true
True or false: If a confidence interval does not contain μ0, we can reject the null hypothesis in a two-tailed test for the same values of α.
true
True or false: In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
true
A confidence interval can be used to test a hypothesis if the hypothesis test is
two-tailed and α stays the same.
The test statistic for population variance depends on the degrees of freedom, sample variance, and the hypothesized population ___________
variance
When evaluating the variability of repair costs of a certain automobile, the population _________ is an important component
variance
A p-value is defined as the probability that
we observed this sample mean (or one more extreme) assuming the null is true.
A Type II error is similar to a false negative for a medical test, that is,
when the null hypothesis states that a patient does not have a virus, the physician fails to reject the null and the patient has the virus.
A Type I error is similar to a false positive for a medical test, that is,
when the null hypothesis states that a patient does not have a virus, the physician rejects the null hypothesis and the patient was healthy.
A sample proportion p is calculated by
x/n
A Type I error is commonly denoted by the symbol
α (alpha)
Which of the following is true?
α = the probability of committing a Type I error; β = the probability of committing a Type II error.
Using the critical value method for a two-tailed test, the critical value is determined by a tail area equal to
α/2
