WARM – UP The campaign manager for a local candidate for city manager wants to determine if his candidate will win. He collected an SRS of 250 voters and then constructed a 95% Confidence interval from the sample proportion of 53% and margin of error of 3.2%. Interpret the margin of error, m. Calculate the two values of the interval ( ). Interpret the 95% Conf. Interval constructed in (b). ) The true proportion of votes the candidate will receive will be within 3.2% of the estimate of 53%. (0.53 ± 0.032) = (49.8%, 56.2%) We are 95% confident (sure) that the true proportion of votes the candidate will receive is between 49.8% and 56.2% of the votes.

QUIZ REVIEW Describe a Sampling Distribution for: a.) Proportions b.) Means Verify all three assumptions for: a.) Proportions (see Distribution Sheet) b.) Means 3. Find the probability for: a.) Proportions b.) Means Central Limit Theorem- Calculate margin of error: Calculate a confidence Interval.

Rogers was interested in determining the true proportion of residents opposed to a city dump being placed in the neighborhood. He collected an SRS of 200 residents and found 86% were opposed. Calculate and interpret the 95% Confidence Interval. 95% .835 .885 .910 .810 .785 .935 .86 I am 95% Confident that the true population proportion of residents opposed to the new dump is between 81.0% and 91.0%.

95% Confidence Interval = 90% Confidence Interval = Critical Value – is the number z* with probability p lying to the right under the standard normal. This is called the Upper p critical value. C% P P -z* z* where z* is the upper (1 – C)/2 critical value found by: z* = | INVNORM( (1 – C)/2 ) | or by Table What are the z* for: 95% Confidence Interval = 90% Confidence Interval = 99% Confidence Interval = z* = 1.960 z* = 1.645 z* = 2.576

company vehicles are fuel efficient? EXAMPLE: A large national company wants to keep costs down so it purchases fuel efficient vehicles. An SRS of 40 vehicles are selected and it is found that 28 of them are classified “Fuel Efficient”, what percent of the entire company vehicles are fuel efficient? 1. Estimate the population parameter with a 90% Confidence Interval and Interpret it. 2. Estimate the population parameter with a 99% Confidence Interval and Interpret it. We can be 90% confident that the true population proportion of fuel efficient vehicles in the company is between 58.1% and 81.9%.

company vehicles are fuel efficient? EXAMPLE: A large national company wants to keep costs down so it purchases fuel efficient vehicles. An SRS of 40 vehicles are selected and it is found that 28 of them are classified “Fuel Efficient”, what percent of the entire company vehicles are fuel efficient? 2. Estimate the population parameter with a 99% Confidence Interval and Interpret it. We can be 99% confident that the true population proportion of fuel efficient vehicles in the company is between 51.3% and 88.7%.

HW: PAGE 448: 22-25 a) b.) I am 90% confident that the true proportion of live births for women under 40 is between 0.188 & 0.286. c.) In Repeated Sampling, 90% of constructed intervals will capture the true proportion of live births. d.) No! 25% is in the interval.

HW: PAGE 448: 22-25

The proportion of married men in their 20’s has changed since the 1950’s. To estimate today’s proportion, a random sample of 60 men in their 20’s was taken to find: Construct a 95% Confidence interval to estimate the percent of married men in their 20’s. Construct a 99.7% Confidence interval to estimate the percent of married men in their 20’s.

CONFIDENCE INTERVALS Confidence Level – A level C confidence interval for a parameter is an interval computed from sample data by a method that in repeated sampling has probability C of producing an interval containing the true value of the parameter. True Parameter An 85% Confidence Level

Collected by an SRS - Stated Approximately Normal by: Large n & C.L.T. EXAMPLE: The weight of a bag of Potato Chips is supposed to have mean = 20.4 oz with std. dev.= 1.24 oz. The product is declared underweight if it weighs less than 18 oz which is stated on the bag. With a SRS sample of 34 bags find the probability that the Product will be underweight. Collected by an SRS - Stated Approximately Normal by: Large n & C.L.T.