24 Questions
| Total Attempts: 1592

Quantitative Methods II

Questions and Answers

- 1.The expected value of the difference of two sample means equals the difference of the corresponding population means:
- A.
Only if the populations are normally distributed

- B.
Only if the samples are independent

- C.
Only if the populations are approximately normal and the sample sizes are large

- D.
All of the above

- 2.In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference is normal if:
- A.
The sample sizes are both greater than 30

- B.
The populations are normal

- C.
The populations are non-normal and the sample sizes are large

- D.
All of the above

- 3.In testing for differences between the means of two independent populations the null hypothesis is:
- A.
H0: μ1-μ2=2

- B.
H0: μ1-μ2=0

- C.
H0: μ1-μ2>0

- D.
H0: μ1-μ2

- 4.When testing
*H*0*: μ*1*-μ*2*=0*vs.*H*1*: μ*1*-μ*2*<0*, the observed value of the*z*-score was found to be –2.15. The*p*- value for this test would be:- A.
.0158

- B.
.0316

- C.
.9842

- D.
.9684

- 5.In testing for differences between the means of two dependent populations the null hypothesis is:
- A.
H0: μD=2

- B.
H0: μD=0

- C.
H0: μD

- D.
H0: μD>0

- 6.The symbol
*xD*refers to:- A.
The difference in the means of two dependent populations

- B.
The difference in the means of two independent populations

- C.
The matched pairs differences

- D.
The mean difference in the pairs of observations taken from two dependent samples

- 7.The quantity
*s²p*is called the pooled variance estimate of the common variance of two unknown but equal population variances. It is the weighted average of the two sample variances, where the weights represent the:- A.
Sample variances

- B.
Sample standard deviations

- C.
Sample sizes

- D.
Degrees of freedom for each sample

- 8.If we are testing for the difference between the means of 2 dependent populations (matched pairs experiment) with samples of
*n*1=15 and*n*2=15, the number of degrees of freedom is equal to:- A.
29

- B.
28

- C.
14

- D.
13

- 9.Two samples of sizes 25 and 35 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom of the equal-variances
*t*-test statistic is:- A.
60

- B.
59

- C.
58

- D.
35

- 10.Given the information:
*s²*1*=4, s²*2*=6, n*1*=15, n*2*=25*the number of degrees of freedom that should be used in the pooled – variance*t*test is:- A.
40

- B.
38

- C.
15

- D.
25

- 11.In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows:
*n*1*=25, x*1*=7.30, s*1*=1.05,n*1*=15, n*2*=25, x*2*=6.80, and s*2*=1.20*. Assume that the population variances are equal. Then, the standard error of the sampling distribution of the sample mean difference*x*1*- x*2is equal to:- A.
0.1017

- B.
1.2713

- C.
0.3189

- D.
1.1275

- 12.In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be known and the calculated test statistic equals 2.56. If the test is two-tail and 5% level of significance has been specified, the conclusion should be to:
- A.
Reject the null hypothesis

- B.
Not to reject the null hypothesis

- C.
Choose two other independent samples

- D.
None of the above

- 13.A political analyst in Texas surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans. This would be an example of:
- A.
Independent samples

- B.
Dependent samples

- C.
Independent samples only if the sample sizes are equal

- D.
Dependent samples only if the sample sizes are equal

- 14.In testing for differences between the means of two dependent populations where the variance of the differences is unknown, the degrees of freedom are:
- A.
N – 1

- B.
N1+n2-1

- C.
N1+n2-2

- D.
N - 2

- 15.In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if the populations are normal with equal variances.
- A.
True

- B.
False

- 16.In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be known, and the calculated test statistic equals 2.75. If the test is two-tail and 5% level of significance has been specified, the conclusion should be not to reject the null hypothesis.
- A.
True

- B.
False

- 17.Both the equal-variances and unequal variances test statistic and confidence interval estimator of require that the two populations be normally distributed.
- A.
True

- B.
False

- 18.When testing for differences between the means of two dependent populations, we can use either a one-tailed or two-tailed test.
- A.
True

- B.
False

- 19.Tests in which samples are not independent are referred to as matched pairs.
- A.
True

- B.
False

- 20.Repeated measurements from the same individuals is an example of data collected from matched pairs experiment.
- A.
True

- B.
False

- 21.A statistics professor wanted to test whether the grades on statistics test were the same for upper and lower classmen. The professor took a random sample of size 12 from each and conducted a test determining that the variances were equal. For this situation, the professor should use a matched pairs
*t*-test.- A.
True

- B.
False

- 22.In comparing two means when samples are dependent, the variable under consideration is
*xD*, where the subscript*D*refers to the difference.- A.
True

- B.
False

- 23.When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for is Student
*t*distributed with degrees of freedom, provided that the differences are normally distributed.- A.
True

- B.
False

- 24.A Marine drill instructor recorded the time in which each of 10 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a
*t*-distribution with 9 degrees of freedom.- A.
True

- B.
False

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