Warm-upDay of 8.1 and 8.2 Review

8.2 P#20, 23 and 24

P#20 a. and b.

c. Since the p-hat is along the line forreasonably likelyevents.

3

2tothatcompare

40

23ˆ opp

8.2 Type of ErrorsThe logic of guilty or not guilty works when thinking aboutwhether to reject or fail to reject the null hypothesis.

When understanding errors in hypothesis testing, itis best to think of medical tests to determine if adisease is present.

Other ways to remember.

Normally you start with the idea that the null hypothesis is true, andthat the person is healthy. So your first mistake would be to reject thenull hypothesis or to declare the person diseased. This would be yourType I error.When do Type I errors occur?They occur when you have the bad luck of drawing an unusualsample. Also when you choose a significance level (α) this also createsthe probability of making a Type I error.

Power and Type II Errors βA test’s ability to detect a false hypothesis is its power.When the null hypothesis is actually false, we hope ourtests is strong enough to reject it. So β is the probabilitythat the test fails to rejected a false null hypotheses.

Power = 1- β . Whenever a study fails to reject its null hypothesis, the test’s power comes into question.

Power is the test’s ability to reject the null hypothesis. This is important when the null hypothesis if false.

Reducing both Type I and Type II errorsReduce the likelihood of a Type II error byincreasing sample size OR increasing the level ofsignificance.

Discussion QuestionsPg 506 of textbookD36. Explain why an increase in sample size increases the

power of a test, all else remaining unchanged.Hint: Think about it, as if the null hypothesis was notcorrect.D37. What happens to the power of a test as the population

proportion, p, moves farther away from the hypothesized value, p0, all else remaining unchanged?

Skip D38.

Explanation of D 36 and D 37

If it was false, thelarger standard dev.of th smaller samples,increase the probability of a Type II error.

Power – the ability of thetest to accurately reject the null hypothesis.

8.1 to 8.2 Review in classAs part of a quality improvement program, your mailorder company is studying the process of filling customerorders. According to company standards, an order is shippedon time if it is sent within 3 working days of the time it isreceived. You select a simple random sample (SRS) of 100 ofthe 5000 orders received in the past month for an audit. Theaudit reveals that 86 of these orders were shipped on time.Find a 95% confidence interval for the true proportion of themonth’s orders that were shipped on time.

Finish #2 and #3 in the next 15 minutes. If you finish early start the homework.8.2 E #26 and 27 and # 34

2.The estimate is 0.86, SE = 0.0347 so the 95% CI is0.7920 to 0.9280.2.a) H0: p = .384 HA: p > .384 where p is the proportion of all

free throws that Sue makes this season.b) The test statistic is Z = 3.13.c) The P-value is 0.0009. Reject the null hypothesis for a =

0.05; also at a = 0.01.d) .4991 to .7509. There is strong evidence that Sue has

improved.e) We must assume that the shots are equivalent to a random

sample from all shots. Also, the sample size must be sufficiently large (which it is).

Work for P-value or Step #3 in a significance test

Answers continued…3.The estimate is .173 with SE = .0437, so the 95% CI is

0.0877 to 0.2590.

For the Quiz. Know all the vocabulary. Know the steps, conditions.

Know how to find the confidence interval with your calculator AND by showing your work.

Know how to do a one proportion z test with your calculator AND how to show your work for Part 3.

Directions for Quiz

• Read the problems carefully.• Follow the steps reviewed in class for #2.• For #2, set up the alternate hypothesis as not

equal to the proportion pH A

Answer to a.of A.P. Question continued…Confidence Interval

Interpretation of interval

Interpretation of confidence level

Answers to parts b. and c. b.

c.