1. Type I and Type II Errors Part 2

2. Recall.. Type-I Error—Null is true and we reject it.
Type II Error—Null is false and we fail to reject it.

3. Alpha Level
The level of significance is the maximum probability of committing a Type I Error symbolized by the Greek letter Alpha.
Three arbitrary values are typically (though not required) used, .1, .05, & .01

4. Beta
Beta is the chance of a Type-II Error symbolized by the Greek letter beta.
It is not easily computed (and will not be for this class)

5. Rejection region
The “critical value” separates the critical from the non-critical region, symbolized by CV.
The critical or rejection region is the probability area “past” the critical value. It will be a z-score greater than a right tailed test and less than a left-tailed test
Recall that if the test is two-sided, we will half each of the critical regions.

6. Trade-offs between alpha and beta
Decreasing the likelihood of a Type I error increases the chance of a Type II
Decreasing the likelihood of a Type II increases the chance of a Type I

7. Recall the confidence interval
The mean for the number of cyclist that wear a helmet in Florida is 60%. Last year, there were 781 accidents and 396 wore helmets. With 90% confidence, what is the confidence interval of our sample?

8. Mechanics
𝒑 = 𝟑𝟗𝟔 𝟕𝟖𝟏 𝒐𝒓 .𝟓𝟎𝟕
𝑺𝑬 𝒑 = .𝟓𝟎𝟕∗.𝟒𝟗𝟑 𝟕𝟖𝟏 = .𝟎𝟏𝟕𝟗
𝑴𝑬 𝒑 =±𝟏.𝟔𝟒∗.𝟎𝟏𝟕𝟗= ±.𝟎𝟐𝟗𝟒
We are 90% confident, the mean of our population is between & .5364
Try this with the (STATS, TEST, “alpha A” 1-PropZint Test” to verify the results

9. now let’s do this with a hypothesis test
𝐻 0 :𝜇= .6
𝐻 𝑎 :𝜇< .6 Alpha at -.1
𝜎 𝑝 = .6∗ = .0175
𝑧= .507− =−5.3
NormalCdf(-99,-5.3) =
Since our P-Value is significantly lower than our CV Alpha value, we reject the null. There is a significant decrease in the number of cyclist that wear helmets.

10. Please verify..
Please check this result with the “Stats, Test, item 5--<1-PropZTest>