500 câu trắc nghiệm Kinh tế lượng – 6A

14) A group of 56 randomly selected students have a mean score of 30.8 with a standard deviation of 4.5 on a placement test. What is the 90 percent confidence interval for the mean score, \(\mu \), of all students taking the test?
○ 29.2 < \(\mu \) < 32.4
○ 29.4 < \(\mu \) < 32.2
○ 29.6 < \(\mu \) < 32.0
● 29.8 < \(\mu \) < 31.8

Use the margin of error, confidence level, and standard deviation \(\sigma \) to find the minimum sample size required to estimate an unknown population mean \(\mu \).
15) Margin of error: $139, confidence level: 95%, \(\sigma \) = $513
○ 5
● 53
○ 46
○ 3
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.
16) 99%; n = 17; \(\sigma \) is unknown; population appears to be normally distributed.
○ \({z_{\alpha /2}}\) = 2.575
● \({t_{\alpha /2}}\) = 2.921
○ \({t_{\alpha /2}}\) = 2.898
○ neither

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.
17) A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.
○ $492.52 < \(\mu \) < $835.76
○ $493.71 < \(\mu \) < $834.57
● $453.59 < \(\mu \) < $874.69
○ $455.65 < \(\mu \) < $872.63

Solve the problem.
18) A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size n = 20 from the population. The population is normally distributed and \(\sigma \) is unknown. When constructing the confidence interval, the researcher should use the t distribution; however, she incorrectly uses the normal distribution. Will the true confidence level of the resulting confidence interval be greater than 95%, smaller than 95%, or exactly 95%?
● Smaller than 95%
○ Exactly 95%
○ Greater than 95%

Find the appropriate minimum sample size.
19) You want to be 95% confident that the sample variance is within 40% of the population variance.
○ 224
○ 11
○ 14
● 56
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 amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.4 15.7 15.2 15.8
15.8 15.4 15.0 15.6
Find a 98 percent confidence interval for the population standard deviation \(\sigma \).
○ (0.17, 0.60)
○ (0.18, 0.60)
● (0.18, 0.69)
○ (0.20, 0.79)