One Prop Z-Test

StepsOne Proportion Z Interval Pp = proportion of _________ who _____________ CRandom: SRS Normality: Independence: pop ≥ 10n FOne Prop Z Interval (_____, ______) SWe are ______% confident that the interval captures the true proportion of __________ who _________.

StepsOne Proportion Z Test Pp = proportion of _________ who _____________ H 0 : p = ______ H a : p ______ CRandom: SRS Normality: Independence: pop ≥ 10n FOne Prop Z Test Z = ________ p = ________ S Since p α, we reject/fail to reject H 0. We conclude/cannot conclude that __________________________.

I say “Normal” you say _________________. So, the calculator is calculating a Z score based on the sampling distribution of Then, it uses Table A to calculate the probability. We are lucky. We have calculators. Yay, TI.

A potato-chip producer has just received a truckload of potatoes from its main supplier. If the producer determines 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 a significance test at the α = 0.10 significance level. What should the producer conclude?

Remind me, what is a p-value??? In the context of the last problem, describe the following: Type I Error Type II Error Power

I claim that I am an 80% free throw shooter. You think I am overestimating my ability and challenge me to a 50 shot trial. In my trial, I make only 32 shots. Is the difference statistically significant at the α = 0.05 level ? What if α = 0.01?

At the conclusion of a significance test, we have made a decision. We either reject H 0 or we fail to reject H 0. But, we’re left wondering, what is a good estimate of the true value of p (the population proportion)? A confidence interval can shed light on this!

According to the Centers for Disease Control and Prevention (CDC) Web site, 50% of high schoolstudents have never smoked a cigarette. Jasonwonders whether this national result holds true inhis large, urban high school. For his AP Statisticsclass project, Jason surveys an SRS of 150students from his school. He gets responses fromall 150 students, and 90 say that they have neversmoked a cigarette. What should Jason conclude?Give appropriate statistical evidence to supportyour answer.

For his AP Statistics class project, Jason surveys an SRS of 150 students from his school. He gets responses from all 150 students, and 90 say that they have never smoked a cigarette. Construct a 95% confidence interval for p, the proportion of students at Jason’s school who say they have never smoked a cigarette. Don’t forget to recheck the normality condition!

Confidence Intervals and Two-Sided Tests There is a link between confidence intervals and two-sided tests. The 95% confidence interval gives an approximate range of p 0 ’s that would not be rejected by a two-sided test at the α = 0.05 significance level. The link isn’t perfect because the standard error used for the confidence interval is based on the sample proportion, while the denominator of the test statistic is based on the value p 0 from the null hypothesis. A two-sided test at significance level α (say, α = 0.05) and a 100(1 – α )% confidence interval (a 95% confidence interval if α = 0.05) give similar information about the population parameter. If the sample proportion falls in the “fail to reject H 0 ” region, like the green value in the figure, the resulting 95% confidence interval would include p 0. In that case, both the significance test and the confidence interval would be unable to rule out p 0 as a plausible parameter value. However, if the sample proportion falls in the “reject H 0 ” region, the resulting 95% confidence interval would not include p 0. In that case, both the significance test and the confidence interval would provide evidence that p 0 is not the parameter value.

A two-sided test of H 0 : p = p 0 at significance level α gives roughly the same conclusion as a 100(1 – α )% confidence interval. CAUTION: This duality does not apply to one- sided significance tests and confidence intervals!

From the output above, see if you can identify H 0 and H a All the necessary components of the “formula” step The conclusion (reject or fail to reject) The duality between the CI and the hypothesis test