AP Stats: 9.1/9.2: Two-sided tests, confidence intervals ...

[Pages:5]AP Stats: 9.1/9.2: Two-sided tests, confidence intervals, errors and significance Name: 2016-2017 Warm Up A potato-chip producer has just received a truckload of potatoes from its main supplier. If the producer finds convincing evidence that more than 8% of the potatoes in the shipment have blemishes, the truck will be sent away to get another load from the supplier. A supervisor selects a random sample of 500 potatoes from the truck. An inspection reveals that 47 of the potatoes have blemishes. Carry out the first three steps at the = . significance level. (As a class, we will advise the producer regarding what conclusion to draw)

Two-sided tests example (Example from last time) According to the Centers for Disease Control and Prevention (CDC) Web site, 50% of high school students have never smoked a cigarette. You wonder whether this national result holds true in large urban high schools. You survey an SRS of 150 students from such a school. From all 150, 90 say they have never smoked a cigarette. What should you conclude?

With two-tailed tests, to compute the P-Value__________________________________________________ (using the test statistic) and __________________________; since is split between two tails, the P-Value has to be acknowledged in each tail by doubling it

AP Stats: 9.1/9.2: Two-sided tests, confidence intervals, errors and significance Name: 2016-2017 Confidence Intervals Well, then, what interval does capture the true proportion of students at the large urban high school who smoke?

Notice, what does this interval have to do with the significance test?

As long as the confidence interval and the two-sided test have levels which are "_________________________," they give similar information about the population parameter.

Oops. We draw conclusions based on the data we have. Hopefully our conclusion is correct, but there is the possibility that our conclusion is wrong. Type 1 Error: Type 2 Error:

AP Stats: 9.1/9.2: Two-sided tests, confidence intervals, errors and significance Name: 2016-2017 Errors Example 1 A company has developed a new deluxe AAA that is supposed to last longer than its regular AAA battery. However, these new batteries are more expensive to produce, so the company would like to be convinced that they really do last longer. Based on years of experience, the company knows that its regular AAA batteries last for 30 hours of continuous use, on average. The company selects an SRS of 15 new batteries and uses them continuously until they are completely drained. The sample mean lifetime is = 33.9 hours. A significance test is performed.

Describe a Type I and Type II error. Describe the consequences of each.

Errors Example 2: Back to the potato-chip producer example In your groups, be ready to...

Identify the Type 1 Error. Describe the consequences. Identify the Type II Error. Describe the consequences.

AP Stats: 9.1/9.2: Two-sided tests, confidence intervals, errors and significance Name: 2016-2017 Errors Fun facts #1 The probability of a type I error is the probability of rejecting Ho when it is actually true. If you think about it, this is exactly ________________________________________________________.

#2 The probability of avoiding a type II error is called the Power close to 0 means the test has almost no chance of correctly detecting that the null

is false. A power near 1 means the test is very likely to reject Ho in favor HA of when Ho is false.

In comparison... The significance level of attest is the probability of reaching the ________________________

conclusion when the null hypothesis is true. The power of a test to detect a specific alternative is the probability of reaching

the_______________________ conclusion when the alternative is true.

Power and Type II Error The power of a test against any alternative is 1 minus the probability of a Type II error for that alternative: Power = ________________________________________________

How to increase the power of a significance test: 1. _____________________________________________

More information is always better, so that the difference between the null and alternative is smaller. 2. _______________________________________________

Increasing , or the probability of a Type 1 error, decreases the probability of a Type II error (and vice versa)

3. ____________________________________________ that is important to detect between the null and alternative parameter values.

AP Stats: 9.1/9.2: Two-sided tests, confidence intervals, errors and significance Name: 2016-2017 Power Examples

1. Which is more serious for the potato-chip producer in this setting: a type I error or a Type II error?

Based on your answer, would you choose a significance level of = 0.01, 0.05, 0.10? Why?

2. Tell if each of the following would increase or decrease the power of the test. Justify your answers.

Change the significance level to = 0.10

Take a random sample of 250 potatoes instead of 500 potatoes.

Let's look at an example from the text, 9.2: #58: What is Power? Read for context. a. Explain in simple language what "power = 0.23" means in this setting.

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