# 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 $\pi$.

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



6. How would the distribution of $\hat{\pi}_n$ change if $\pi$ increased?





7. What do you notice about the distribution of $\hat{\pi}_n$ from the simulation?





## Standard deviation

8. How does the standard deviation of $\hat{\pi}_n$ change as $n$ increases?



## Normal approximation

9. Write down the 68-95-99 rule



## Confidence intervals

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



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



12. 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 $\pi$?