- Calculate and interpret confidence intervals for estimating a population mean.
- Understand the roles of sample size, confidence level, and spread on the margin of error.

- Population vs Sample
- Parameter vs Statistic
- Point Estimates:
- The sample mean `barx` is an estimate for the population mean `mu`.
- The sample proportion `p'` is an estimate for the population proportion `p`.
- The sample standard deviation `s` is an estimate for the population standard deviation `sigma`.

- Interval Estimates:
- The average age of college students is between 21.24 and 29.56.

The average age of a college student is within 4.16 years of 25.4. - The proportion of females attending college is between 43% and 63%.

The proportion of female college students is within 10% of 53%.

- The average age of college students is between 21.24 and 29.56.
- Sampling Distribututions

aka a histogram of sample means,

or a histogram of sample proportions.

`"margin"=("right"-"left")/2`

`"point estimate"=("right"+"left")/2`

OR

`"left"="point estimate"-"margin"`

`"right"="point estimate"+"margin"`

- Average Body Temperature: `mu`

Interval estimate: `98.048^circ F < mu < 98.468^circ F` or `(98.048^circ F, 98.468^circ F)`

Point estimate: `barx = 98.258^circ F` and `EBM=0.210^circ F`

`mu = 98.258^circ F +- 0.210^circ F` - Average Restaurant Tip: `mu`

`$3.478 < mu < $4.232` or `($3.478, $4.232)`

`barx=$3.855` and `EBM=$0.377`

`mu = $3.855 +- $0.377`

**Interpretation:**

We are 95% confident that the average daily tip at this restaurant is between $3.48 and $4.23.

- Calculate and interpret confidence intervals for estimating a population proportion.
- Understand the roles of sample size, confidence level, and spread on the margin of error.

- Proportion of peanuts in a can of mixed nuts: `p`

Interval estimate: `0.42 < p < 0.62` or `(0.42, 0.62)`

Point estimate: `hat p = p' = 0.52` and `EBP=0.10`

`p = 0.52 +- 0.10` - Proportion of home game wins for a soccer team: `p`

`0.492 < p < 0.675` or `(0.492, 0.675)`

`hat p = p' = 0.583` and `EBP=0.091`

`p = 0.583 +- 0.091`

**Interpretation:**

We are 95% confident that proportion of home game wins for this soccer team is between 49.2% and 67.5%.

A realization of 50 confidence intervals attempting to capture that actual population mean.

The confidence level is NOT a chance of success!

Which of the following statements best describes a 95% confidence level?

- 95% of people's body temperatures are in this interval.
- There is a 95% chance that a randomly selected person will be in the interval.
- There is a 95% chance that the average human body temperature will be in this interval.
- 95% of similar intervals will contain the actual mean human body temperature.

Notice that as the sample size increases, the standard deviation of the sampling distribution decreases.

Female College Students: `x=48`, `n=100`, and the standard error is about 0.049.

Female College Students: `x=479` , `n=1000`, and the standard error is about 0.016.

Female College Students: `x=3501` , `n=7313`, and the standard error is about 0.0058.