1. AP Statistics Friday, 05 February 2016 OBJECTIVE TSW review for Monday’s test on confidence intervals. ASSIGNMENT DUE –WS AP Review: Confidence Intervals (z)  wire basket ASSIGNMENT DUE MONDAY –WS AP Review: z & t Confidence Intervals with Means

2. WS Confidence Intervals #2 1)a)Assumptions * SRS (given) * Distribution is approximately normal (n ≥ 30) * σ is known We are 99% confident that the true mean time that general managers spend with their current companies is between 11.0080 years and 12.5520 years. b)A sample size of 68 hotel managers would be needed to estimate the mean within ± 1 year with 99% confidence.

3. WS Confidence Intervals #2 2)a)The shape is approximately normal, as evidenced by the approximately linear quartile plot. b)Assumptions * SRS (assumed) * Approximately normal distribution (approximately linear quantile plot) * σ is known We are 95% confident that the true mean measurement lies between 223.9706 mm and 224.0294 mm. c)A sample size of 35 crankshafts would be needed to estimate the mean within 0.020 mm.

4. WS Confidence Intervals #2 3)a) The station’s calculations are correct. It’s estimate of $8669 falls within the 95% confidence interval. b)It is unknown if their conclusion describes the population of all the city’s citizens. The station’s sample probably contains voluntary bias, which could affect the true mean pay increase.

5. WS Confidence Intervals #1 1)a)1.2816 b)2.0537 c)3.0902 2)a)The shape is normal because the sample size is more than 30. b)Assumptions: * SRS * Normal distribution (n > 30) *  is known We are 90% confident that the true mean score of basic arithmetic and the ability to apply it is in the interval (252.2579, 277.7421).

6. WS Confidence Intervals #1 2)c) d)“95% confidence” means that the method used to construct an interval will produce intervals that contain  95% of the time. 3)a)The shape is normal because the sample is large (n > 30). b)Assumptions: * SRS * Normal distribution (n > 30) *  is known We are 90% confident that the true mean yield (bushels per acre) is in the interval (119.0983, 127.5617).

7. WS Confidence Intervals #1 3)c) d) e)As the confidence level increases, the margins of error also increase.

8. Test Topics: Confidence Intervals Construct a confidence interval from a given level of confidence. –  known z* –  unknown t* – Always include assumptions, calculations, AND conclusion. “We are --% confident that the true mean of lies within the interval. Determine sample size to obtain a given margin of error.

9. Test Topics: Confidence Intervals Determine critical value: – z* Blue chart: Find p in the table, determine the corresponding z-score Calculator: invNorm(p) – t* Degrees of freedom (df) = sample size (n) – 1 Green chart (B): – Find CL at the bottom and df on the left side: cv = intersection point Calculator: invT(p, df)

10. Test Topics: Confidence Intervals Determine normality of a distribution – Given (the problem explicitly states, “normal distribution”) – Sample size (n) ≥ 30 – Graph shows normality Histogram – Approximately symmetrical Boxplot – Approximately symmetrical Quantile plot – Approximately linear Vocabulary – Standard error – Margin of error – Robust (An inference procedure is ROBUST if the confidence level or p-value doesn’t change much if the assumptions are violated.) Know the characteristics of confidence intervals – “What happens when...”

11. WS: AP Review – Confidence Intervals (z) 1) C 2) C 3) E 4)B 5) A 6) E 7) D 8)C

12. WS: AP Review – z & t Intervals with means 1) D8) E 2) B9) D 3) A10) B 4)B11) D 5) C12) B 6) E13) A 7) C