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Download 10-4 Sampling Distribution for Two Sample Means
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SWBAT: Create the Sampling distribution for the difference between two Means Lesson 10-4 Do Now: How do we describe the sampling distribution for the difference between two proportions? Shape: Center: Spread: The Sampling Distribution of − Choose an SRS of size n1 from Population 1 with mean μ1 and standard deviation σ1 and an independent SRS of size n2 from Population 2 with mean μ2 and standard deviation σ2 . Shape: Center: Spread: SWBAT: Create the Sampling distribution for the difference between two Means Lesson 10-4 Example: Based on information from the U.S. National Health and Nutrition Examination Survey (NHANES), the heights of ten-year-old girls follow a Normal distribution with mean μf = 56.4 inches and standard deviation σf = 2.7 inches. The heights of ten-year-old boys follow a Normal distribution with mean μm = 55.7 inches and standard deviation σm = 3.8 inches. A researcher takes a random sample of 12 ten-year-old girls and a separate random sample of 8 ten-year-old boys in the United States. After analyzing the data, the researcher reports that the mean height X m of the boys is larger than the mean height X f of the girls. (a) Describe the shape, center, and spread of the sampling distribution of − . (b) Find the probability of getting a difference in sample means − that’s less than 0. Show your work. (c) Does the result in part (a) give us reason to doubt the researcher’s stated results? Explain. SWBAT: Create the Sampling distribution for the difference between two Means Lesson 10-4 You Try!! A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine’s manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27 ounces and standard deviation 0.8 ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17 ounces and standard deviation 0.5 ounces. To test the manufacturer’s claim, the restaurant manager measures the amount of liquid in a random sample of 25 cups filled with the medium setting and a separate random sample of 20 cups filled with the large setting. Let − be the difference in the sample mean amount of liquid under the two settings (large − medium). (a) Describe the sampling distribution of − ? (b) Find the probability that − is more than 12 ounces. Show your work. (c) Based on your answer to Question (b), would you be surprised if the difference in the mean amount of liquid dispensed in the two samples was 12 ounces? Explain. SWBAT: Create the Sampling distribution for the difference between two Means Lesson 10-4 LESSON PRACTICE 1. The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean 170 mg/dl and standard deviation 30 mg/dl. Suppose we select independent SRSs of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean heights ̅ and ̅ . (a) Describe the shape, center, and spread of the sampling distribution of ̅ − ̅ . (b) Find the probability of getting a difference in sample means ̅ − ̅ that’s less than 0 mg/dl. Show your work. (c) Should we be surprised if the sample mean cholesterol level for the 14-year-old boys exceeds the sample mean cholesterol level for the men? Explain. SWBAT: Create the Sampling distribution for the difference between two Means Lesson 10-4 2. The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights ̅ and ̅ . (a) Describe the shape, center, and spread of the sampling distribution of ̅ − ̅ . (b) Find the probability of getting a difference in sample means ̅ − ̅ that’s greater than or equal to 2 inches. Show your work. (c) Should we be surprised if the sample mean height for the young women is more than 2 inches less than the sample mean height for the young men? Explain.
