Business Stats Chapter 9 Smartbook
The critical value of z for a right-tailed test with α = .10 is
+1.28
The critical value of z for a left-tailed test with α = .05 is
-1.645
A 95% confidence interval could be used to conduct a two-tailed hypothesis test when alpha is
.05
A left-tailed hypothesis test for a mean resulted in tcalc = -1.50 with df = 29. The p-value would be in what range?
.05 < p-value < .10
For a two-tailed test of a proportion, zcalc = 1.30. The p-value is
.1936
Power is represented by
1-β
For the following hypotheses and sample result choose the correct conclusion: H0: μ ≥ 67 vs. H1: μ < 67. z critical = - 1.28 and zcalc = -1.04.
Fail to reject the null hypothesis and conclude that there is not significant evidence to state μ < 67.
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.
True or false: An alternative hypothesis should never have an equal sign.
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
In order to calculate the power a hypothesis test for a mean, the following information must be known:
an alternative value for μ a known or estimated value for σ significance level, α
For a given sample size, reducing α results in an
increase in β.
The critical value stated in the decision rule is determined by
level of significance
To find the two-tailed p-value for a test statistic tcalc using Excel use the following formula:
=t.dist.2t(tcalc, df)
Given the following hypotheses: H0: π ≤ .25 vs. H1: π > .25, zcalc = 2.30. The p-value is _____
Blank 1: .0107
For a two-tailed test with zcalc = -1.80, the resulting p-value is
Blank 1: .0718 or .0719
For a right-tailed test with zcalc = 1.45, the p-value is _____ (Round to four decimals)
Blank 1: .0735
For a two-tailed test with zcalc = 0.78, the resulting p-value is ______ . (Round to four decimals.)
Blank 1: .4354 or .4353
Given that β = .23 for a particular set of hypotheses, power =
Blank 1: .77
______ testing is used by business managers to guide decision making.
Blank 1: Hypothesis
A hypothesis is also known as an
Blank 1: assumption or theory
An OC curve stands for _____ / _____ curve.
Blank 1: operating Blank 2: characteristic
True or false: A proportion can be expressed as percentage but not all percentages can be expressed as a proportion.
True
A test statistic is
a standardized score of a sample statistic.
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−8.5(s32)x-8.5s32, with df = 31
The critical value of z for a two-tailed test with α = .01 is
±2.576
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.
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
The p-value is calculated assuming the
the null hypothesis is true.
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.
Hypothesis testing is used to test _____ and _____ in business and science
Blank 1: assumptions Blank 2: theories
The parameter value in the null hypothesis is called a ______ and the value does not come from a _______
Blank 1: benchmark Blank 2: sample
Hypothesis testing uses sample _____ to test assumptions
Blank 1: 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
Blank 1: fail Blank 2: to Blank 3: reject
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.)
Blank 1: forty or 40
The greater the difference between the true value of the population parameter and the null hypothesis benchmark value the _____ the value of power.
Blank 1: greater, higher, or more
A hypothesis, or assumption, can be discarded or reformulated if the sample data is found to be _______ with the hypothesis
Blank 1: inconsistent or in conflict
Alpha (α) is known as the significance ______ and defines the rejection _____ in tailed test
Blank 1: level Blank 2: region or area
The critical value is determined by the chosen _______ of ______
Blank 1: level Blank 2: significance or alpha
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.
Blank 1: multiply or times Blank 2: two or 2
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_____
Blank 1: robust Blank 2: outliers
Reject the null hypothesis and conclude that the population proportion is less than .25.
False
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
True or false: All statistically significant result have practical importance.
False
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
A business wants to use sample data to confirm that their average processing times have decreased after installing updated equipment. Their alternative hypothesis would be
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
Match the change in the parameter to the effect on power.
Increase in power <--> Choice Increase in n , Choice Increase in α Decrease in power <--> Increase in σ
In hypothesis testing, there are 2 possible incorrect decisions:
Not rejecting the null hypothesis when it is false. Rejecting the null hypothesis when it is true.
As the sample size, n, increases
P(Type II error) decreases. power increases.
Suppose a hypothesis test resulted in a p-value = .0456. Match the significance level to the correct conclusion.
Reject H0 -- α = .10 , Choice α = .05 Fail to reject H0 -- α = .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.
Given the following hypotheses: H0: π ≥ .25 vs. H1: π < .25, zcalc = -1.30 and the p-value is .0968. The level of significance is .10. Which is the appropriate conclusion?
Reject the null hypothesis and conclude that the population proportion is less than .25.
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.
In hypothesis testing, there are 2 possible incorrect decisions:
Rejecting the null hypothesis when it is true. Not rejecting the null hypothesis when it is false.
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.
Which variables below would express proportion data?
The number of customers who agree that the new product price is acceptable. The number of employees who reported an accident last month.
Which variables below would express proportion data?
The number of employees who reported an accident last month. The number of customers who agree that the new product price is acceptable.
Which variables below would express proportion data?
The number of employees who reported an accident last month. The number of customers who agree that the new product price is acceptable.
True or false: All business managers need a basic understanding of hypothesis testing.
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
True or false: We choose a value for α before conducting a hypothesis test.
True
The significance level is the probability of making a
Type I error (α)
We would not reject the null hypothesis when the p-value is
close to 1.0 greater than the level of significance.
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
A statistical hypothesis test requires that we
determine whether it is a one- or a two-tailed test. identify the population parameter of interest.
True or false: In the critical value approach, if a test statistic falls outside of the rejection region, then we can reject the null hypothesis.
false
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.
All other things being equal, power will increase when the sample size _____
increases
We can generally reduce the probability of Type II errors by
increasing the sample size.
The p-value method for testing hypotheses is often preferred by statisticians because
it is more flexible than the critical value method. it expresses the strength of your evidence against the null.
the _____ the p-value, the more inclined we are to reject the null hypothesis.
lower
Increasing the value of alpha in a hypothesis test will
make it less difficult to reject the null hypothesis,
The p-value is the probability of obtaining a sample mean as extreme as the one observed, assuming the ______ hypothesis is true
null
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 definition of power is
rejecting the null hypothesis when the null is false.
The test statistic used for testing μ when the population mean, σ, is unknown is
tcalc = xbar -Uo / Sl rootn*
The difference between the sample statistic and the null hypothesis value is measured by a
test statistic.
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)
The critical z value is
the z value that separates the rejection region from the non-rejection region. the z value associated with level of significance.
All business managers need a basic understanding of hypothesis testing because
they are required to read and understand technical reports. they often interact with specialists. they must make decisions based on statistical evidence.
True or false: All business managers need a basic understanding of hypothesis testing.
true
A confidence interval can be used to test a hypothesis if the hypothesis test is
two-tailed and α stays the same.
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 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.
We can reject the null hypothesis
when the p-value < α.
A sample proportion p is calculated by
x/n
A sample proportion p is calculated by
xn
The test statistic for testing a mean when sigma is known is computed by the formula
z=x−μ0σ/n√
The test statistic for the hypothesis test of the population proportion p is
zcalc = p−π0π0(1−π0)n o-pi0 ________ sqrt* x0(1-x0) ---- 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
