Stat 1040
Chapter 23 Solutions

    1. True.
    2. True.
    3. False - it's a confidence interval.

  2. The data are like 1000 draws from a box with 50,000 tickets. Each ticket shows the commute distance for the head of the household. The SD of the box is unknown, but we can estimate it using the SD of the sample, as 9.0 miles. The SE of the sum is sqrt{1000}*9.0 = 285 miles. The SE of the average is 285/1000 = 0.3 miles. The data do not follow the normal curve, but the average of 1000 draws will follow the normal curve, so we can obtain confidence intervals.
    1. 8.7 miles, 0.3 miles.
    2. 8.7 miles plus or minus 0.6 miles. (8.1,9.3) miles.

    1. We cannot do it - we need to use the 2-sample method.
    2. The SE of the average is approximately 1.

    1. True.
    2. True.
    3. Probably false - the data do not follow the normal curve.
    4. False - 325 is the SE not the SD.
    5. False - the normal curve is used for confidence intervals.

  5. 1.7 plus or minus 0.1. (1.6, 1.8).

    1. True.
    2. False - there is no such thing as a CI for the sample average.
    3. True.
    4. False - that used the SE, and also, there must be a whole number of people.
    5. False - if it did, there would be many households with a negative number of people.
    6. True.

  7. There is too much spread - the SE of the average is only 0.3, and for that histogram the SE is closer to 1.

  8. This is not a confidence interval - there is no sample. At best, the ``sample'' is a sample of convenience, so we cannot find confidence intervals.