500 câu trắc nghiệm Kinh tế lượng – 6C

Solve the problem.
14) When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the following finite population correction factor: \(\sqrt {\frac{{N – n}}{{N – 1}}} \)

Find the 95% confidence interval for the mean of 200 weights if a sample of 37 of those weights yields a mean of 150.2 lb and a standard deviation of 24.2 lb.
○ 142.4 lb < \(\mu \) < 158.0 lb
○ 144.1 lb < \(\mu \) < 156.3 lb
○ 143.1 lb < \(\mu \) < 157.3 lb
● 142.9 lb < \(\mu \) < 157.5 lb

Do one of the following, as appropriate: (a) Find the critical value \({z_{\alpha /2}}\), (b) find the critical value \({t_{\alpha /2}}\), (c) state that neither the normal nor the t distribution applies.
15) 90%; n = 9; s = 4.2; population appears to be very skewed.
● Neither the normal nor the t distribution applies.
○ \({z_{\alpha /2}}\) = 1.645
○ \({z_{\alpha /2}}\) = 2.365
○ \({t_{\alpha /2}}\) = 1.860

Use the given degree of confidence and sample data to construct a confidence interval for the population mean \(\mu \). Assume that the population has a normal distribution.
16) Thirty-five randomly selected students took the calculus final. If the sample mean was 82 and the standard deviation was 5.3, construct a 99 percent confidence interval for the mean score of all students.
● 80 < \(\mu \) < 84
○ 79 < \(\mu \) < 85
○ 78 < \(\mu \) < 86
○ 81 < \(\mu \) < 83

Solve the problem.
17) A simple random sample of students is selected, and the students are asked how much time they spent preparing for a test. The times (in hours) are as follows: 1.3 7.2 4.2 12.5 6.6 2.5 5.5
Based on these results, a confidence interval for the population mean is found to be \(\mu \) = 5.7 ± 4.4. Find the degree of confidence.
○ 95%
● 98%
○ 99%
○ 90%

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation \(\sigma \). Assume that the population has a normal distribution.
18) To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval for the population standard deviation \(\sigma \).
○ 0.13 < \(\sigma \) < 0.22
● 0.12 < \(\sigma \) < 0.24
○ 0.11 < \(\sigma \) < 0.25
○ 0.15 < \(\sigma \) < 0.21

Find the appropriate minimum sample size.
19) To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population’s standard deviation, the number of observations within the data set must be greater than or equal to what quantity?
○ 805
○ 335
○ 250
● 191

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation \(\sigma \). Assume that the population has a normal distribution.
20) The daily intakes of milk (in ounces) for ten randomly selected people were:
27.4 14.9 11.1 22.8 14.2
10.5 12.8 13.7 21.5 23.2
Find a 99 percent confidence interval for the population standard deviation \(\sigma \).
○ (3.67, 12.16)
○ (3.55, 12.16)
● (3.67, 13.54)
○ (0.87, 3.36)