# Exercise: estimation and confidence intervals

#Objective We did this exercise on the first day talking about estimation. It builds on the quiz from last week when the students had a problem asking for the mean and variance of $\frac{1}{2}(X+Y)$, where $X$ and $Y$ are independent random variables, each following a $N(2,3^2)$ distribution.

This exercise went really well. There were enough familiar elements that students didn’t get stuck often, but enough new stuff to keep the discussion going. Students were explaining concepts to each other and stretching for the meaning of the confidence interval, which was awesome to see.

By the way, I initiated this exercise before ever talking about confidence intervals. We’re moving that direction very soon, though…

# Exercise

## Overview

We will sample some data relating to the profit (in cents) per gallon of gas at gas stations nationally, and use the data to estimate the expected profit per gallon. This exercise is similar to a quiz question from last week.

## Calculations

Assume that the population follows a normal distribution and that the variance is 9 ${\rm cents}^2$ (standard deviation is 3 cents). You will be pulling ten samples from the population, each independent and with identical distribution, and then calculating the mean of your ten samples.

- What are the variance and standard deviation of the sample mean?

## Sampling

Now your group should come to the front and take ten samples (with replacement), writing each one down.

- Why do you think I had you replace each chip after sampling?
*(hint: what is the population for each sample, and what would it be if you didn’t return the chips?)* - The ink I used today is non-permanent, so be gentle with the chips to avoid wiping off data.
- There is writing on both sides - today’s data are the more delicate numbers.

## Point estimation

Return to your seats and calculate the mean of your sample. Using your calculations from earlier, sketch the distribution of the sample mean (you may assume that it is Normal).

## Interval estimation

Use the table to calculate the central interval with 50% probability mass. Shade this region on your sketch and label the end points.

- What is your interpretation of the meaning of the shaded interval?
*(hint: it has to do with confidence)*.

## 21 Comments

## vudedb

<a href=http://propecial.com>acheter propecia</a>

propecia prescription coupons http://propecial.com

## affzov

<a href=http://canadian-pharmacyon.com>buy generic viagra online</a>

buy viagra super active http://canadian-pharmacyon.com

## givlbo

<a href=http://canadian-pharmacyon.com>viagra 60 pills</a>

is viagra online real http://canadian-pharmacyon.com

## zjgzen

<a href=http://cialisn.com>buy generic cialis online</a>

best place buy cialis online http://cialisn.com

## dsficd

<a href=http://canada-pharmaci.com>how much does cialis cost</a>

cialis pills to buy http://canada-pharmaci.com

## vgfplj

where to buy viagra in us http://canadian-pharmacie.com

## fvwcoh

viagra levitra online http://canadian-pharmacya.com

<a href=http://camadian-pharmacya.com>order viagra</a>

## Jazesglolf

levitra 10mg how long does it last joined http://levitragtr.com - levitra 20 mg price levitra in kuwait levitra levitra 20 mg price - levitra herbal equivalent buy levitra online dogpile web search

## hlnhch

is there a true generic viagra http://canadian-pharmacyon.com

<a href=http://canadian-pharmacyon.com>buy viagra online usa</a>

## zqocwy

<a href=http://levitranew.com>cheap generic levitra online</a>

le levitra est il en vente libre en espagne http://levitranew.com

## glgbbk

<a href=http://canada-pharmaci.com>is it safe to buy cialis online</a>

cialis originale online http://canada-pharmaci.com

## zosivq

<a href=http://canadian-pharmasy.com>cheapest cialis professional</a>

dove acquistare cialis online http://canadian-pharmasy.com

## benqmp

<a href=http://canadian-pharmasy.com>buy cialis las vegas</a>

cialis http://canadian-pharmasy.com

## asniqr

best generic viagra in india http://canadian-pharmacya.com

<a href=http://camadian-pharmacya.com>buy viagra usa</a>

## bsqxma

mail order viagra legitimate http://canadian-pharmacyon.com

<a href=http://canadian-pharmacyon.com>buy viagra pills</a>

## phmydd

<a href=http://propecial.com>how does propecia work</a>

propecia gegen geheimratsecken http://propecial.com

## zdckqy

<a href=http://cialisn.com>buy cialis online canada pharmacy</a>

cialis price walmart http://cialisn.com

## zlsdfx

farmacia online cialis 10 mg http://canadian-pharmasy.com

<a href=http://canadian-pharmasy.com>canadian pharmacy cialis</a>

## bwcmnl

cheap cialis pills online http://canada-pharmaci.com

<a href=http://canada-pharmaci.com>how can i buy cialis online</a>

## guszvj

viagra price reduction http://canadian-pharmacie.com

<a href=http://canadian-pharmacie.com>brand viagra 48 pills</a>

## lawpyd

<a href=http://cialisn.com>buying cialis online</a>

comprar cialis 20 mg online http://cialisn.com