Confidence Intervals and Population Size Review

Which z-value is used for a 95% confidence interval?

• 1.65
• 1.96
• 2.58
• 2.33

Given the same mean, SD, and sample size, a confidence interval of 80% would be wider than a confidence interval of 90%

• True
• False

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. What type of interval would this be?

• z interval

• t interval

• 1-prop z interval

• None of these.

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.

A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement μ in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which one of the following is a correct interpretation of this confidence interval?

• Ninety percent of the 85 sixth-graders in the sample improved their reading comprehension scores by 12.6 to 14.8 points.
• The probability is 0.90 that the true mean improvement in reading comprehension is between 12.6 and 14.8.
• We are 90% confident that the true improvement in reading comprehension scores is captured by the interval 12.6 to 14.8.

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?

• We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre

• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.

• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.

A radio talk show host is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to 18. To find this proportion, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to 18?” He asks listeners to phone in and vote “yes” or “no” depending upon their opinions. Of 200 people who phone in, 140 answer “yes.” What type of interval should be used?

• z interval

• t interval

• 1-prop z interval

• none of these

A random sample of size n is collected from a Normally distributed population with standard deviation σ. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used?

• Using a higher confidence level
• Using a lower confidence level
• Using a smaller sample size n

The heights (in inches) of adult males on a small Pacific Island are believed to be Normally distributed with an unknown mean μ. The average height of a random sample of 55 adult males from the island is found to be 69.72 inches, with a sample standard deviation of s = 4.15 inches. What kind of confidence interval should be used?

• z interval

• t interval

• 1 prop z interval

You are thinking of using a z procedure to construct a 95% confidence interval for the unknown mean μ of a population for a random sample taken from the population. You suspect that the distribution of the population is not Normal and may in fact be moderately skewed. Which of the following statements is then correct?

• You should not use the z procedure, since the population does not have a Normal distribution.

• You can use the z procedure provided that n>30 .

• You can use the z procedure regardless of the sample size since z procedures are robust against non-Normality.