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Ch. 10
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Terms in this set (37)
Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample.
False
The difference between the two sample means xbar1-xbar2 is an interval estimator of the difference between two population means µ1-µ2.
False
For a statistical inference regarding xbar1-xbar2, it is imperative that the sampling distribution of µ1-µ2 is normally distributed.
True
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution xbar1-xbar2 of is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1+n2 ≥ 30.
False
The confidence interval for the difference µ1-µ2 is based on the same approach used in the case of one sample: Point Estimate ± Standard Error.
False
The margin of error in the confidence interval for the difference µ1-µ2 equals the standard error SE(xbar1-xbar2) multiplied by either za/2 or t a/2,df
or , depending on whether or not the population variances are known.
True
In the case when ø21 and ø22 are unknown and can be assumed equal, we can calculate a pooled estimate of the population variance.
True
We convert the estimate xbar1-xbar2 into the corresponding value of the z or t test statistic by dividing the difference between xbar1-xbar2 and the hypothesized difference d0 by the standard error of the estimator xbar1-xbar2.
True
The necessary condition for a matched-pairs sample is that the same individual gets sampled twice.
False
We always deal with matched-pairs sampling if two samples have the same number of observations.
False
Two or more random samples are considered independent if
-The process that generates one sample is completely separate from the process that generates the other sample
The choice of an appropriate test for comparing two population means depends on whether we deal with
-Qualitative or quantitative data
-Independent or matched-pairs sampling
-The equality or lack of equality of population variances
Which of the following is not a restriction for comparing two population means?
The equality of the sample sizes
When comparing two population means, their hypothesized difference
May assume any value
Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?
Independent sampling with quantitative data
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of is xbar1-xbar2 approximately normal only if both sample sizes are sufficiently large—that is, when
n1 ≥ 30, n2 ≥30
Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?
H0: µ1-µ2 ≥ 0
HA: µ1-µ2 < 0
A demographer wants to measure life expectancy in countries 1 and 2. Let µ1 and µ2 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.
H0: µ1-µ2 ≥ -10
HA: µ1-µ2 < -10
When calculating the standard error of xbar1-xbar2, under what assumption do you pool the sample variances s12 and s22 ?
Unknown population variances that are assumed equal
What formula is used to calculate the degrees of freedom for the t test for comparing two population means when the population variances are unknown and unequal?
...
In the test for comparing two population means when population variances are unknown and unequal, a student calculates the degrees of freedom using the proper formula as 34.7. How many degrees of
freedom should the student assume to find the p-value of the test?
34
When testing the difference between two population means under independent sampling, we use the z distribution if
The population variances are known
If the sampling distribution of xbar1-xbar2 cannot be assumed normal, we
Are unable to compute a confidence interval
Assume the competing hypotheses take the following form: H0: µ1-µ2=0 versus HA: µ1-µ2≠0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed with known variances and we use independent sampling. The value of the appropriate test statistic is computed as
...
Assume the competing hypotheses take the following form: H0: µ1-µ2=0 versus HA: µ1-µ2≠0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and we use
independent sampling. The population variances are not known and cannot be assumed equal. The value
of the appropriate test statistic is computed as
...
Assume the competing hypotheses take the following form: H0: µ1-µ2=0 versus HA: µ1-µ2≠0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also
assume that the populations are normally distributed and that the observations in the two samples are independent. The population variances are not known but are assumed equal. The value of the appropriate test statistic is computed as
...
What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?
A t test under dependent sampling
A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?
A matched pairs hypothesis test for μD.
What type of data is required to compare prices of the same textbooks sold by two different vendors?
Dependent random samples with quantitative data
Which of the following set of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling?
H0: µd ≥ 0
HA: µd < 0
What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?
Independent sampling with qualitative data
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant
hypotheses are constructed as
H0: p1-p2 ≤ 0
HA: p1-p2 > 0
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let men and women be represented by populations 1 and 2, respectively. The relevant
hypotheses are constructed as
H0: (p1-p2) ≥ 0
HA: p1-p2 < 0
It is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling:
only if n1pbar1 ≥ 5, n1(1-pbar1) ≥ 5, n2pbar2 ≥ 5 and n2(1-p2) ≥ 30.
When the hypothesized difference of the population proportions is equal to 0, we
-are able to estimate the standard error of p1-p2, using the pooled pbar
-can use the confidence interval to implement the test if the difference of the population proportions is equal to 0.
A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. In order to qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?
A hypothesis test for p1-p2
A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. In order to qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications. Let and represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default, respectively.
HO: p1-p2 ≥ 0
HA: p1-p2 < 0
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