Confidence Intervals Assessment

If the 95% confidence interval of the proportion of the population is (.10,.50), which of the following is NOT correct?

• If the sample size were to increase the width of the interval would decrease.

• We are 95% confident that the true proportion is 30% because it is the middle of the interval.

• An increase in confidence level generally results in an increase in the width of the confidence interval.

• If you would like a smaller confidence interval, you could decrease the confidence level.

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CCSS.HSS.IC.B.4

Which of the following is true about constructing confidence intervals?

• Margin of error for a 95% confidence interval is determined by multiplying 2 times the standard error.

• The center of the confidence interval is the population parameter.

• One of the values that changes the width of a confidence interval is the population size.

• If the value of the population parameter is known, it is important to calculate a confidence interval for it.

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CCSS.HSS.IC.B.4

What is the point estimator for the interval (-5 , 13)?

• 10

• 9.5

• 9

• -5

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CCSS.HSS.IC.B.4

What is the margin of error for the interval (6.8, 12.9)?

• 9.85

• 3.05

• 3.50

• 6.8

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CCSS.HSS.IC.B.4

A 95% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 95% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144

• We are 95% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.

• 95% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144

• We are 95% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

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CCSS.HSS.IC.B.4

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10.

What is the point estimate for the population mean?

• 75

• 105.2

• 10

• 0.90

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CCSS.HSS.IC.B.4

The lifetime of a certain type of battery is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.44, 125.76)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

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CCSS.HSS.IC.B.4

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• Yes

• No

• Not enough information

• I have no idea what you're asking of me

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CCSS.HSS.IC.B.4

The standard IQ test has a mean of 97 and a standard deviation of 18. We want to be 95% certain that we are within 5 IQ points of the true mean. Determine the required sample size.

• 8

• 50

• 1

• 147

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CCSS.HSS.IC.B.4

The standard IQ test has a mean of 95 and a standard deviation of 17. We want to be 95% certain that we are within 2 IQ points of the true mean. Determine the required sample size.

• 1

• 373

• 278

• 17

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CCSS.HSS.IC.B.4