AP Statistics T Intervals

The heights of 5-year old boys are approximately normal. The mean height of a random sample of 37 5-year old boys is found to be 30 inches with a standard deviation of 3 inches. What is the standard error of x̄?

• .493

• 1.32

• 5.77

• 1.96

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores. Suppose that you do this many, many times. Which of the following are the mean and standard deviation of the sampling distribution of x̄ ?

• Mean = 515; SD = 114

• Mean = 515; SD = 114/√100

• Mean = 515/100; SD = 114/√100

• Mean = 515/100; SD = 114/100

• Mean = 515/100; SD = 114/√100

Which of the following would not decrease the width of a confidence interval?

• I only

• II only

• III only

• I and II only

• II and III only

What does this symbol represent?

• population proportion

• parameter

• sample proportion

• population sample

The 90% interval for a statistics test was given by 72 +- 7. What is the lower bound for the interval?

• 7

• 72

• 65

• 79

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What would NOT be a condition we need to verify before constructing the interval?

• np̂ ≥ 10 and n(1-p̂) ≥ 10

• n ≥ 30

• 10% condition

• random sample

Why is it important to check the 10% condition before calculating probabilities involving x̄?

• To reduce the variability of the sampling distribution of x̄

• To ensure that the distribution of x̄ is approximately Normal

• To ensure that we can generalize the results to a larger population

• To ensure that x̄ will be an unbiased estimator of μ.

• To ensure that the observations in the sample are close to independent.

A friend has placed a large number of plastic disks in a hat and invited you to select one at random.  He informs you that half are red and half are blue.  If you draw a disk, record the color, replace it, and repeat 100 times, which of the following is true?

• It is unlikely you will choose red more than 50 times.

• If you draw 10 blue disks in a row, it is more likely you will draw a red on the next try.

• The overall proportion of red disks drawn should be close to 0.50.

• The chance that the 100th draw will be red depends on the results of the first 99 draws.

The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes.  What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?

• 0.9678

• 0.0322

• 0.0344

• 0.3851

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population.  Which of the following would produce a wider confidence interval, based on these same data?

• Use a larger confidence level

• Use a smaller confidence level

• Use the same confidence level, but compute the interval n times.  Approximately 5% of these intervals will be larger

• Increase the sample size