Interpreting Confidence Intervals

​Confidence Intervals

Multiple Choice

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• 1.799

• 1.798

• 1.803

Multiple Choice

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. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Margin of Error to two decimal places.

• 1.90

• 1.89

• 1.899

• 1.99

Multiple Choice

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a sample standard deviation of $950. Construct a 99% confidence interval for the repair cost. 

• (1069.77, 2530.23)

• (1077.13, 2522.87)

• (1167.15, 2432.85)

• None of these.

Multiple Choice

A 90% 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.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144

• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 

• There is a 90% chance that CEOs in the electronics industry have salaries that fall between $139,048 to $154,144

• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

Multiple Choice

An inspector monitors large truckloads of potatoes to determine the proportion p of potatoes with major defects before the potatoes are used to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects a simple random sample of 50 potatoes from a truckload of more than 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Which one of the following assumptions for inference about a proportion using a confidence interval is violated?

• Large counts.

• 10% condition.

• There are not violations.

Multiple Choice

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

Multiple Choice

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

• 9.85

• 3.05

• 3.50

• 6.8

Choosing the correct inference procedure

​Qualitative or Quantitative

One Sample or Two Samples

Test or Estimate

T or Z

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