500 câu trắc nghiệm Kinh tế lượng – 6B

Use the margin of error, confidence level, and standard deviation \(\sigma \) to find the minimum sample size required to estimate an unknown population mean \(\mu \).
14) Margin of error: $136, confidence level: 99%, \(\sigma \) = $545
○ 54
○ 62
● 107
○ 11
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) 91%; n = 45; \(\sigma \) is known; population appears to be very skewed.
○ \({z_{\alpha /2}}\) = 1.75
● \({z_{\alpha /2}}\) = 1.70
○ \({t_{\alpha /2}}\) = 1.645
○ \({t_{\alpha /2}}\) = 1.34

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) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.
○ 69.2 < \(\mu \) < 83.2
○ 64.2 < \(\mu \) < 88.2
○ 74.6 < \(\mu \) < 77.8
● 67.7 < \(\mu \) < 84.7

Solve the problem.
17) 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 known. When constructing the confidence interval, the researcher should use the normal distribution; however, she incorrectly uses the t distribution. How does this incorrectly calculated confidence relate to the correct confidence interval?

● The calculated confidence interval is wider than the correct confidence interval.
○ The calculated confidence interval is narrower than the correct confidence interval.
○ The calculated confidence interval is shifted to the right of the correct confidence interval.
○ The calculated confidence interval is shifted to the left of the correct confidence interval.

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) The mean replacement time for a random sample of 20 washing machines is 9.5 years and the
standard deviation is 2.4 years. Construct a 99% confidence interval for the standard deviation, \(\sigma \), of the replacement times of all washing machines of this type.
○ 1.7 yr < \(\sigma \) < 3.8 yr
○ 1.6 yr < \(\sigma \) < 4.6 yr
● 1.7 yr < \(\sigma \) < 4.0 yr
○ 1.7 yr < \(\sigma \) < 5.0 yr

Find the appropriate minimum sample size.
19) You want to be 99% confident that the sample standard deviation \(\sigma \) is within 5% of the population standard deviation.
● 1,335
○ 923
○ 2,638
○ 2,434

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 football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
11 11 7 6 10
6 10 15 12 13
Find a 95 percent confidence interval for the population standard deviation \(\sigma \).
● (2.1, 5.5)
○ (0.7, 2.2)
○ (2.1, 5.0)
○ (2.0, 5.0)