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500 câu trắc nghiệm Kinh tế lượng – 8B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the computer display to solve the problem.
14) When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1) comes from a population with a mean that is less than the mean for the placebo population? Explain.

Trắc nghiệm Kinh tế lượng 4

Yes, the P-value for a one-tail test is 0.0384, which is smaller than the significance level of 0.05. There is sufficient evidence to support the claim that the mean for the treatment group is smaller than the mean for the placebo group.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is \({\mu _d}\) = 0. Compute the value of the t test statistic.
15) A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below.

Plot: 1 2 3 4 5 6 7 8 9 10
Before 9 9 8 7 6 8 5 9 10 11
After 10 9 9 8 7 10 6 10 10 12

You wish to test the following hypothesis at the 10 percent level of significance.

Ho: \({\mu _D}\) = 0 against H1: \({\mu _D}\) ≠ 0.

What is the value of the appropriate test statistic?
● 5.014
○ 2.033
○ 1.584
○ 2.536

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.
16) Suppose you wish to test the claim that \({\mu _d}\), the mean value of the differences d for a population of paired data, is greater than 0. Given a sample of n = 15 and a significance level of \(\alpha \) = 0.01, what criterion would be used for rejecting the null hypothesis?
○ Reject null hypothesis if test statistic < 2.624. ○ Reject null hypothesis if test statistic > 2.602.
○ Reject null hypothesis if test statistic > 2.977 or < -2.977. ● Reject null hypothesis if test statistic > 2.624.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.
17) A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course.

Before 74 83 75 88 84 63 93 84 91 77
After 73 77 70 77 74 67 95 83 84 75

Test statistic t = 2.366. Critical values: t = ± 2.262.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the mean is not affected by the course.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a confidence interval for \({\mu _d}\, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
18) Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. Construct a 90% confidence interval for the mean of the differences.

Before 33 33 38 33 35 35 40 40 40 31
After 34 28 25 28 35 33 31 28 35 33

○ 2.5 < \({\mu _d}\ < 7.1
○ 1.5 < \({\mu _d}\ < 8.1
○ 3.8 < \({\mu _d}\ < 5.8
● 1.8 < \({\mu _d}\ < 7.8

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Test the indicated claim about the variances or standard deviations of two populations. Assume that the populations are normally distributed. Assume that the two samples are independent and that they have been randomly selected.
19) Two types of flares are tested for their burning times (in minutes) and sample results are given below. Use a 0.05 significance level to test the claim that the two brands have equal variances.

Brand X Brand Y
n = 35 n = 40
\({\bar x}\) = 19.4 \({\bar x}\) = 15.1
s = 1.4 s = 0.8

H0: \(\sigma _1^2\) = \(\sigma _2^2\). H1: \(\sigma _1^2\) > \(\sigma _2^2\).
Test statistic: F = 3.0625. Critical value: F = 1.9429.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two brands have equal variances.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
20) When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted FR. The lower critical F value, FL , can be found as follows: interchange the
degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR can be denoted \({F_{\alpha /2}}\) and FL can be denoted \({F_{1- \alpha /2}}\).

Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:

n1 = 9, n2 = 7, \(\alpha \) = 0.05
● 0.2150, 5.5996
○ 0.2150, 4.8232
○ 0.3931, 4.1468
○ 0.2411, 4.1468