diff --git a/book/.DS_Store b/book/.DS_Store index 34d8f78..9648286 100644 Binary files a/book/.DS_Store and b/book/.DS_Store differ diff --git a/book/_build/.doctrees/confidenceintervals.doctree b/book/_build/.doctrees/confidenceintervals.doctree index 21e9bbf..dda9ff1 100644 Binary files a/book/_build/.doctrees/confidenceintervals.doctree and b/book/_build/.doctrees/confidenceintervals.doctree differ diff --git a/book/_build/.doctrees/environment.pickle b/book/_build/.doctrees/environment.pickle index f4aa910..bdf9e73 100644 Binary files a/book/_build/.doctrees/environment.pickle and b/book/_build/.doctrees/environment.pickle differ diff --git a/book/_build/html/_sources/confidenceintervals.md b/book/_build/html/_sources/confidenceintervals.md index 2e6b66c..d2e5b53 100644 --- a/book/_build/html/_sources/confidenceintervals.md +++ b/book/_build/html/_sources/confidenceintervals.md @@ -80,3 +80,33 @@ name: bernoulliCLT2wCI Each miniature histogram reflects $n=400$ coin flips where $p=0.2$. Grayed out histograms are those where the confidence interval misses the true parameter. ``` +## The Accuracy of Averages + +Proportions are a special kind of average. The sample average $\bar{x}$ estimates the population average $\mu$. For general averages, there is no formula analogous to SD=$\sqrt{p(1-p)}$. The standard deviation must be estimated from the data. With a large simple random sample, the SD of the sample is a good estimate of the SD of the box. Then, the SE for the average can be calculated + +$$\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.$$ + +Once the SE is found, a confidence interval is constructed like in the case of proportions. For example, a 95% confidence interval is $\bar{x} \pm 2\text{SE}$. + +## Exercises + +```{exercise-start} +:label: CIicecream +``` +In a survey of 96 randomly selected Americans, $\hat{p} = 0.60$ said they think ice cream should be banned. Find the 95% confidence interval for the proportion. +```{exercise-end} +``` + +```{exercise-start} +:label: CInarrow +``` +You are interested in the 95% confidence interval of a sample mean. Which of the following makes this interval more narrow? + +1. More observations. +2. Fewer observations. +3. Higher value of the average. +4. Lower value of the average. +5. Both 1 and 4 +```{exercise-end} +``` + diff --git a/book/_build/html/confidenceintervals.html b/book/_build/html/confidenceintervals.html index 47e4a34..b25f6e7 100644 --- a/book/_build/html/confidenceintervals.html +++ b/book/_build/html/confidenceintervals.html @@ -427,6 +427,8 @@

Contents

+
  • The Accuracy of Averages
    • +
  • Exercises
    • @@ -502,6 +504,37 @@

    Interpretation of a Confidence Interval +

    The Accuracy of Averages#

    +

    Proportions are a special kind of average. The sample average \(\bar{x}\) estimates the population average \(\mu\). For general averages, there is no formula analogous to SD=\(\sqrt{p(1-p)}\). The standard deviation must be estimated from the data. With a large simple random sample, the SD of the sample is a good estimate of the SD of the box. Then, the SE for the average can be calculated

    +
    +\[\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.\]
    +

    Once the SE is found, a confidence interval is constructed like in the case of proportions. For example, a 95% confidence interval is \(\bar{x} \pm 2\text{SE}\).

    + +
    +

    Exercises#

    +
    + +

    Exercise 40

    +
    +

    In a survey of 96 randomly selected Americans, \(\hat{p} = 0.60\) said they think ice cream should be banned. Find the 95% confidence interval for the proportion.

    +
    +
    +
    + +

    Exercise 41

    +
    +

    You are interested in the 95% confidence interval of a sample mean. Which of the following makes this interval more narrow?

    +
      +

    1. More observations.

      2. +

    2. Fewer observations.

      3. +

    3. Higher value of the average.

      4. +

    4. Lower value of the average.

      5. +

    5. Both 1 and 4

      6. +
    +
    +
    +