Tuesday HW!

Today in class we looked a little more at the interpretations of confidence intervals and did a quick review of the conditions for a one proportion z-interval--these ideas will be assessed on our quiz to start class on Thursday; tonight's homework also gives us the opportunity to practice this stuff in preparation for that quiz.

Tomorrow (and through the rest of the week) we'll start to explore the mathematics of confidence intervals, starting with an exploration of how we calculate a confidence interval.

Tonight, please complete the following in your textbook, OR the questions are posted below:

Page 447: 3a, 13abd, 11(just check conditions)

3a.) Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems. They find that 14 of the 134 cars stopped have at least one safety violation. They want to estimate the percentage of all cars that may be unsafe (have at least one safety violation).

     1. Identify the population and the sample.
     2. Explain what p and p-hat represent.
     3. Determine if we can use a one proportion z interval (check conditions!)

13.) An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.

a.) Create a 95% confidence interval for the percentage of all auto accidents that involve teeenage drivers. Assume the conditions for inference have been satisfied.

• To create the "one proportion z interval" we'll use our calculator...
• Press STAT, scroll over to TESTS
• Choose "OnePropZ-Int"
• Enter x, n, and our confidence level.
• Press calculate and you'll see your interval

b.) Explain what your interval means. (Interpret your interval).

d.) A politician urging tighter restrictions on drivers' license issued to teens says, "In one of every five auto accidents, a teenager is behind the wheel." Does your confidence interval support or contradict this statement? Explain.

• Consider the interval from (a) and what that interval tells us (b)...does our interval suggest that in 1 of every 5 auto accidents a teenager is behind the wheel? Why or why not?

11.) A May 2000 Gallup Poll found that 38% of a random sample of 1,012 adults said they believe in ghosts. This data was used to create a confidence interval to estimate the percent of American adults who believe in ghosts.

Determine if a one proportion z interval is appropriate.

Homework Answer Key:

3a.) KEY

• Population = "all cars" (in the US? in this state? who travel this road? This part is not clear.)
• Sample = the 134 cars that were stopped and checked to see if they had at least one safety violation
• p = the % of all cars that are "unsafe" (have at least one safety violation)
• p-hat = the % of the 134 cars stopped that were deemed unsafe (p-hat = 14/134 = 0.1045 = 10.45%)
• We CAN use a one proportion z interval because:
• We will assume the 134 cars were selected randomly
• 134 < 10% of all cars 
• 134(0.1044) > 10 (or 14 >10) and 134(1-0.1044)>10 (or 120 >10)

13.) KEY

• 13a) 95% Confidence Interval: (0.12685, 0.18586)
• 13b.) We are 95% confident that the true percentage of all auto accidents that involve teenage drivers falls between 12.685% and 18.586% based on this sample of 582 accidents.
• 13c.) **Discuss as a class**

11.) A one proportion z interval IS appropriate because:

• The sample of 1,012 adults was selected randomly.
• 1012 < 10% of all adults in the U.S.
• 1012(0.38) > 10 and 1012(1 - 0.38) > 10