Confidence Intervals

Worksheet 1

Open the interactive version of the normal tables. (Opens a separate browser window.)

  1. Because of slight irregularities that constantly occur on a production line, cars of identical make are not identical in every fashion. One way in which they vary is their gas mileage. Consider the new Toyanda RV4. The car's mechanical operation is based on a current Toyanda model; engineers expect the variation in gas mileage from car to car to have a normal distribution with standard deviation 0.35. What they don't know is the average gas mileage for the RV4. To find out, they take an SRS of 32 RV4s and drive each, recording gas mileage (mpg). The sample mean is 35.28.
    1. Use this data to construct a 90% CI for the mean gas mileage of all RV4s.
    2. Interpret your result.
    3. Compute a 99% confidence interval (same data).
    4. How do the margins of error for your two intervals compare?
    5. An independent consumer agency can only afford to select an SRS of 8 for testing; the sample mean for these 8 is 35.23. What is this agency's 90% CI for the mean gas mileage of all RV4s?
    6. Compare margin of error for the two 90% CIs you've computed.
  2. What is the average playing time of all Jill's CDs? As usual, Jill is too socially involved to take a census. Therefore, she decides to take an SRS of 12 CDs to estimate this average. Her friend Jack tells her that playing times of CDs are approximately normally distributed with standard deviation 4.27 minutes. (Jack has a lot of free time-he's learned this by collecting data from a CD catalog. However, his results for the average playing time of CDs do not apply to Jill's collection. That's because the catalog Jack used carried all kinds of music, while Jill is almost exclusively a fan of hard-core and rave.) Here's the data:
    55.14 46.23 53.85 43.89 42.77 44.71
    44.58 47.77 48.40 50.65 46.33 50.80
    1. What is the response variable?
    2. Identify the population.
    3. Describe the parameter that is of interest to Jill. What is the symbol typically given to this parameter?
    4. Compute the sample mean.
    5. Construct a 98% CI for the mean playing time of all Jill's CDs? What is your margin of error?
    6. Interpret your CI.
    7. Jack's census of the catalog finds a mean playing time of 51.89 minutes. What can we conclude about Jill's CD collection?