Worksheet 22: Estimation

Worksheet 22: Estimation#

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Kissing right#

  1. In the kissing right study, what is the parameter of interest?

  2. For the null hypothesis \(H_0:\pi=0.5\), the p-value is very small. What can we conclude about the null hypothesis?

  3. About 90% of people are right-handed and maybe people are turning their heads towards their dominant hand. How can this be stated as a null hypothesis?

  4. What would be a plausible value of \(\pi\) based on the data (80 out 124 couples turned right)?

Estimation#

The distribution of \(\hat{\pi}_n\) (the sample proportion) depends on the sample size \(n\) and the parameter \(\pi\).

  1. How do you expect the distribution of \(\hat{\pi}_n\) to change if the sample size \(n\) increased?

  2. How would the distribution of \(\hat{\pi}_n\) change if \(\pi\) increased?

  3. What do you notice about the distribution of \(\hat{\pi}_n\) from the simulation?

Standard deviation#

  1. How does the standard deviation of \(\hat{\pi}_n\) change as \(n\) increases?

Normal approximation#

  1. Write down the 68-95-99 rule

Confidence intervals#

  1. Would a 99% confidence interval be bigger or smaller than a 95% confidence interval?

  2. How could we compute a 99% confidence interval?

  3. In ball chasing experiment:

    a. What is the parameter of interest \(\pi\)?

    b. What is the estimate of \(\pi\)?

    c. What is the standard deviation \(\hat{\pi}_n\)?

    d. How would you compute a 95% confidence interval for \(\pi\)?