Day 63 Agenda:

FR QUESTIONS: MIXING UP PROPORTIONS AND MEANS Score for entire question will be 2 out of 4, max. That implies you may get CAWA for parts of the question. RESPONSE #1:

QUESTION #2: RESPONSE #2:

CH 12.2 & 13.2: Tests of 1-Sample and 2-Sample Proportions AP STAT CH 12.2 & 13.2: Tests of 1-Sample and 2-Sample Proportions EQ: What is the difference between a one-sided test for proportions and a two-sided test for proportions?

RECALL: One-Sided Hypothesis for Means Ha:  > ____ Ha:  < ____

Ha: p ≠ ____ Now we’re going to do a two-sided hypothesis test for proportions. Ha: p ≠ ____ p-value is SUM of the tails

Ex. 1 A recent study suggested that 77% of teenagers have texted while driving. A random sample of 60 teenagers in Atlanta was taken and 35 admitted to texting while driving. Is this convincing evidence that the proportion of teens who text while driving is different from 77%? implies “two-tailed”

H0: the true proportion of teenagers who State: H0: the true proportion of teenagers who say they texted while driving is 77% Ha: the true proportion of teenagers who say they texted while driving is not 77% *** Note: ≠ implies “two-tailed” where p = the true proportion of teenagers who admitted to texting while driving

1-sample z test for proportions Plan: 1-sample z test for proportions Conditions: The problem states the 60 teenage drivers were selected randomly. Random --- all teenage > 10(60) drivers Condition met Independence --- NOTE: large counts calculated using p and q, not p-hat and q-hat!! (.77)(60) > 10 (.23)(60) > 10 46.2 > 10 13.8 > 10 Sample size large enough to use approximate normal distribution. Large Counts --- what you expect to happen

Calculations: 60 0.5833 0.05 NOTE: se calculated using p and q, not p-hat and q-hat!!

REMINDER: Must show p-value is doubled so your work EQUALS what the calculator gives you. Area in BOTH tails ***NOTE: You only calculate area in ONE direction. Inequality is determined by the sign of the test-statistic. Show “double“ the probability to account for both tails. This is just for notation. Calculator gives the doubled p-value when worked for p0 ≠ or μo ≠.

Conclusion: Since our p-value of 0.0005 is less than our significance level α = 0.05, we have significant evidence to reject the null. It is plausible to conclude the true proportion of teenagers who have texted while driving differs from 77% sample. Our data is statistically significant.

Create a 95% confidence interval for this data. Why choose 95% for the confidence level? We are 95% confident the true mean proportion of teenagers who have texted while driving is in the interval 45.9% to 70.8%.

What does this tell you about the conclusion you made from the significance test? Since our confidence interval does not capture the proportion of 77% we have evidence to possibly conclude the true proportion of teenagers who have texted while driving differs from 77%. Or say “we have evidence that it is plausible the true …”

In Class Practice: p. 771 #24 a) State: H0: the true proportion of _____________ _________________________________ Ha: the true proportion of ___________ ________________________________   H0: p = _______ Ha: p ≠ _______ Where p = __________________________ first-year college students who identified “being very well off financially” as an important personal goal is 73% first-year college students who identified “being very well off financially” as an important personal goal is not 73% 0.73 0.73 the true population proportion of first-year college students who identified “being very well off financially” as an important personal goal

z 1 proportions Plan __ test for ___ sample ___________ Conditions: The problem states a simple random sample of 200 first year students were surveyed. Random --- Independence --- Large Counts --- population of all 1st year college students > (10)(200) Condition met for independence. Sample size large enough to consider approximately Normal

Do: n = ____ = _____ se = _____ α = ___ ____P(_________) =

Since our p-value of ______ is_________ _______________________________________________________________  ________________________________________________________________________________________________________________________________________________________________ Since the p-value of 0.027 is less than the significance level α = 0.05, we have evidence to reject the null hypothesis. We have evidence that it is plausible for the true proportion of all first-year college students at this university who think being very well-off is important differs from the the national value of 73%. Our data are statistically significant.

In Class Assignment: p. 772 #29 Use alpha = 0.05 p. 776 #35 Use alpha = 0.01

Matched Pairs 2 Sample

Ex. 2 “Would you marry a person from a lower social class than your own?” Researchers asked this question of a sample of 385 white, never-married students at two colleges in the south. We will consider this to be an SRS of white students at southern colleges. Of the 149 men in the sample, 91 said “Yes.” Among the 236 women, 117 said “Yes.” Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

State:

where

Conditions: MEN WOMEN Plan: Random Independence Large Counts The problem states a SRS of 149 white Southern men were surveyed. The problem states a SRS of 236 white Southern women were surveyed. population of all males at southern colleges > (10)(149) Condition met for independence. population of all females > (10)(236) Condition met for independence. Sample size large enough to consider approximately Normal Sample size large enough to consider approximately Normal

This is where “pooling” comes into play!! Do: Formula for z when Pooling Data for 2 Samples See Formula Sheet! This is where “pooling” comes into play!!

Since our p-value of0. 027 is less than our significance level of 0 Since our p-value of0.027 is less than our significance level of 0.05, we have evidence to reject the null. We can conclude there is possibly a difference in the proportion of men and women who say they would marry a person from a lower social class. Our data is statistically significant.

Assignment: p. 812 #25, 27 p. 819 #29, 30 Inference PW #7