HW-pgs. 690, 693 (11.1, 11.3a, 11.4, 11.6)
11.1-11.2 Quiz Tuesday 3-5-13
Ch. 11 Test Wednesday 3-13-13
www.westex.org HS, Teacher Website
2-25-13
Warm up—AP STATS
1. Last year the mean response time for all accidents by the paramedics was 6.7 minutes. Would an SRS with a mean of 6.48 minutes for 400 calls be convincing evidence that response time has dropped this year?
Name______Date______
AP Statistics
Section 11.1 Significance Tests: The Basics
Objectives:
¨ Explain why ______looks for evidence against a claim rather than in favor of the claim
¨ Define ______and ______hypothesis.
¨ Explain the difference between a ______and a ______hypothesis.
Confidence intervals are one of the two most common types of statistical inference. Use a confidence interval when your goal is to estimate a ______. The second common type of inference , called ______, has a different goal: to assess the evidence provided by data about some claim concerning a population.
The basic idea behind significance test is simple: An outcome that would ______happen if a claim were true is good evidence that the claim is ______.
SIGNIFICANCE TEST-______
______
______
HYPOTHESIS-______
______
The results of a test are expressed in terms of ______that measures how well the data and the hypothesis ______. The reasoning of statistical tests, like that of CIs, is based on asking what would happen if we ______the sampling or experiment many times. We again begin with the unrealistic assumption that we know _____, the population standard deviation.
Example 11.2
Cities monitor paramedic response time. The mean response time in one city was μ = 6.7 minutes with a standard deviation of σ = 2 minutes. At the end of the following year, an SRS of 400 calls showed a mean response time of = 6.48 minutes. Does this data provide good evidence that response time has decreased since the previous year? (We will assume that σ = 2 minutes for this year’s calls too.)
· If the claim that μ = 6.7 minutes is true, the sampling distribution of from 400 calls will be approximately Normal (by CLT) with mean μ = 6.7 minutes and standard deviation:
If we looked at a sampling distribution we’d see that our = 6.48 minutes is just over 2 standard deviations below the mean. The probability of getting an less than or equal to 6.48 is just over 1%. So it’s ______(that is, not due to chance or not likely).
· Suppose that after a sampling of 400 response times = 6.61 minutes. Since this is less than 1 standard deviation below the mean of 6.7 minutes this is not convincing evidence of a decrease in response time (about a 16% chance of getting a value this low or lower).
In a few days we’ll talk about how to perform a significance test at a specified significance level to determine if we can reject the null hypothesis.
A ______starts with a statement of the claims we want to compare. In the last example we asked whether the accident response time data are likely if, in fact, there is no decrease in paramedics’ response times. Because the reasoning of tests looks for evidence ______a claim, we start with the claim we seek evidence against, such as “no decrease in response time”. This claim is our ______.
**Usually the ______is a statement of “no effect”, “no difference”, or no change from historical values.**
The claim about the population that we are trying to find evidence for is the ______. The ______suggests that something has changed or is different than expected.
We abbreviate the null hypothesis as _____ and the alternative hypothesis as _____. In the last example we are seeking evidence of a decrease in ______this year. The null hypothesis says “no decrease” on the average in the large population of all calls this year. The alternative hypothesis says “______”.
So the hypotheses are:
where μ is the mean response time to all calls this year. The alternative hypothesis is ______because we are interested only in deviations from the null hypothesis in one direction.
**Hypotheses always refer to SOME POPULATION, not a particular outcome. Be sure to state Ho and Ha in terms of a ______.** Read example 11.3 to see that your alternative hypothesis can be ______.
**The alternative hypothesis should express the hopes or suspicions we have BEFORE we see the data. It is cheating to first look at the data and then frame Ha to fit what the data show.**
11.5 State Your Claims, II Each of the following situations calls for a significance test. State the appropriate null hypothesis Ho and alternative hypothesis Ha in each case. Be sure to define your parameter each time.
(a) In the setting of Example 11.2 (above), the city manager also noted that paramedics arrived within 8 minutes after 78% of all calls involving life-threatening injury last year. Based on this year’s random sample of 400 calls, she wants to determine whether the paramedics have arrived within 8 minutes more frequently this year.
(b) A national study reports that households spend an average of 30% of their food expenditures on restaurants. A restaurant association in your area wonders if the national results apply locally. They interview a sample of households and ask about their total food budget and the amount spent in restaurants.