AP Statistics Chapter 12 Section 1

TestConfidence IntervalFormulasAssumptions 1-sample z-test mean SRS Normal pop. Or large n (n>40) Know 1-sample t-test mean (could also be used for a matched pairs design) SRS < very normal 15 < n < can be used except in the presence of outliers or strong skewness > use regardless of normality 2-sample z-test SRSs Normal pops or n>40 2-sample t-test SRS < very normal 15 < < 40 can be used except in the presence of outliers or strong skewness > use regardless of normality 1-proportion SRS from a pop of interest Pop > 10(n) Test of Sign. C.I. 2-proportion

Means vs. Proportions Compare means when you are working with quantitative variables. Compare proportions when you are working with categorical variables.

1 - proportion How common is the behavior that puts people at risk of AIDS? 2673 random heterosexual adults were interviewed. Of these 170 had more than one sexual partner in the past year. Based on the data, what conclusions can be drawn regarding the percent of adult heterosexuals who have multiple partners?

2- proportions Do Preschool programs for poor children make a difference in later life? 62 children enrolled in a preschool in the late 1960s and a control group of 61 similar children who were not enrolled. At 27 years of age, 61% of the preschool group and 80% of the control group had required the help of a social service agency (mainly welfare) in the previous 10 years.

More than 2 proportions What is the relationship between time spent in extracurricular activities and success in a tough course in college? 123 college students in a chemical engineering course who needed a grade of C or better to advance to the next class – The passing rates were 55% for students who spent < 2 hours per week in extracurricular activities, 75% for those who spent between 2 and 12 hours per week, and 38% for those who spent more than 12 hours per week. Are the differences in passing rates statistically significant?

Important stuff Population proportion Sample proportion A specific value used to replace the unknown p to test the null hypothesis. Usually 0.5

Confidence Interval formula for 1-proportion Test of significance for 1- proportion

Assumptions 1.SRS of a population of interest 2.Population is at least 10 times as large as the sample 3. Test these for the test of significance Test these for the confidence interval

For a test, the null hypothesis state that p has a specified value. For confidence intervals, we use the statistic to estimate the unknown p.

Choosing sample size This involves the sample proportion of successes, we need to guess this value when choosing n. Call this guess p*. p* can be: 1.Chosen based on a pilot study or on past experience with similar studies. OR 2.Use p* =.5. The margin of error is the largest when p* =.5, so this guess is conservative in the sense that if we get any other p when the study is actually done we will get a smaller margin of error than planned.

Some people think that chemists are more likely than other parents to have female children. The Washington State Dept. of Health lists the parents’ occupations on birth certificates. Between 1980 and 1990, 555 children were born to fathers who were chemists. Of these births, 273 were girls. During this period, 48.8% of all births in Washington State were girls. Is there evidence that the proportion of girls born to chemists is higher than the state proportion?

Given that p =.488 the observed proportion of.4919 would occur approx. 43 times out of every 100 just by chance therefore this evidence supports that p =.488. Assumptions: 1.SRS of population of interest 2.Population of chemists > 10(chemists in Washington State) 95% C.I.

Sample Size? What if you wanted to estimate p with 95% confidence and a margin of error no greater than 3%. How large a sample do you need?