Confidence Intervals for Normal and T-Distributions

A 90% confidence interval for the mean m of a population is computed from a random sample and is found to be .  Which of the following could be the 95% confidence interval based on the same data?

• Without knowing the sample size, any of the above answer could be the 95% confidence interval

A Census Bureau report on the income of Americans says that with 90% confidence, the median income of all U.S. households in a recent year was $57,005, with a margin of error of $742.  Which of the following is the most appropriate conclusion?

• 90% of all the samples of this sample size would result in a sample median that falls within $742 of $57,005

The makers of a specialty brand of bottled water claim that their “mini” bottles contain 8 ounces of water.  To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle.  The mean volume was 7.98 ounces and the 95% confidence interval for the true mean volume is 7.93 to 8.03 ounces.  Based on the sample, which of the following conclusions best addresses the maker’s claim?

• Because 7.98 is in the interval, there is convincing evidence, that their claim is correct.

• Because 7.98 is in the interval, there is not convincing evidence, that their claim is incorrect.

• Because 8 is in the interval, there is convincing evidence, that their claim is correct.

• Because 8 is in the interval, there is not convincing evidence, that their claim is incorrect.

• Because 0 is in the interval, there is convincing evidence, that their claim is incorrect.

The weights (in pounds) of three adult males are 160, 215, and 195. What is the standard error of the mean for these data?

• 190

• 27.84

• 22.73

• 16.07

• 13.13

We want to construct a one-sample t interval for a population mean using data from a population with unknown shape. In which of the following circumstances would it be inappropriate to construct the interval based on an SRS of size 14 from the population?

• A stemplot of the data is roughly bell-shaped

• A histogram of the data shows slight-skewness

• A boxplot shows that the values above the median are much more variable than the values below the median

• The sample standard deviation is large

• The sample standard deviation is small

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours.  For a random sample of 45 seniors without part-time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours.  Assuming the conditions are met, which of the following is the correct standard error for a 95% confidence interval for a difference in population means?

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• 
• 
• 
• 

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

• 89.08 < μ < 94.92

• 87.58 < μ < 96.42

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

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 standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

I randomly select 25 students’ Math SAT scores and find the mean to be 600. I know the standard deviation of the population is 50. Find a 95% Confidence Interval.

Identify the Variables

• 25

• σ

• 1.96

• Z

• 600

• n

• 50

• μ

You sample 12 bugs and find the sample mean is 2.40 cm. You are told the standard deviation is 0.2 cm. Find a 95% Confidence Interval.

• 1.96

• n

• .2

• σ

• 2.40

• μ

• 12

• Z