500 câu trắc nghiệm Kinh tế lượng – 8A

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

7) A marketing survey involves product recognition in New York and California. Of 558 New
Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. At
the 0.05 significance level, test the claim that the recognition rates are the same in both states.

H0: p1 = p2. H1: p1 ≠ p2.
Test statistic: z = 0.97. Critical values: z = -1.96, 1.96.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the recognition rates are the same in both states.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct the indicated confidence interval for the difference between population proportions p1 – p2. Assume that the samples are independent and that they have been randomly selected.
8) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the difference between the population proportions p1 – p2.
○ 0.048 < p1 – p2 < 0.112
○ 0.035 < p1 – p2 < 0.125
○ 0.025 < p1 – p2 < 0.135
● 0.032 < p1 – p2 < 0.128

Determine whether the samples are independent or consist of matched pairs.
9) The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug.
○ Matched pairs
● Independent samples

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected.
10) A researcher wishes to determine whether people with high blood pressure can reduce their
blood pressure by following a particular diet. Use the sample data below to test the claim that the treatment population mean \({\mu _1}\) is smaller than the control population mean \({\mu _2}\). Test the claim using a significance level of 0.01.

Treatment Group: n1 = 85 \({\bar x_1}\) = 189.1 s1 = 38.7
Control Group: n2 = 75 \({\bar x_2}\) = 203.7 s2 = 39.2

H0: \({\mu _1}\) = \({\mu _2}\). H1: \({\mu _1}\) < \({\mu _2}\).
Test statistic t = -2.365. Critical value: t = -2.377.
Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the treatment population mean \({\mu _1}\) is smaller than the control population mean \({\mu _2}\).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.

11) Two types of flares are tested for their burning times (in minutes) and sample results are given
below.

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

Construct a 95% confidence interval for the differences \({\mu _X}\) – \({\mu _Y}\) based on the sample data.
○ 3.5 < \({\mu _X}\) – \({\mu _Y}\) < 5.1
○ 3.2 < \({\mu _X}\) – \({\mu _Y}\) < 5.4
● 3.8 < \({\mu _X}\) – \({\mu _Y}\) < 4.8
○ 3.6 < \({\mu _X}\) – \({\mu _Y}\) < 5.0
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the computer display to solve the problem.

12) 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 different from the mean for the placebo population? Explain.

No, the P-value for a two-tail test is 0.0768, which is greater than the significance level of 0.05. There is not sufficient evidence to support the claim that the two population means are different.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

13) The two data sets are dependent. Find \(\bar d\) to the nearest tenth.

○ 0.6
● 0.5
○ 0.7
○ 0.3