Handout 5

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University of Washington *

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MATH 120

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Statistics

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Feb 20, 2024

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pdf

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Uploaded by strodesr

Handout 5 (Practice Final) 1. Go over the following Lecture Notes: • Introduction to Linear Regression (more weight) • Normal Distribution • Foundations for Inference • Inference for Categorical Data (more weight) • Inference for Numerical Data (more weight) 2. Review Quiz 2 thoroughly, answer Key posted on Canvas 3. Review Handouts 3-4 thoroughly, answer Key posted on Canvas 4. Review Homework’s 4-8 thoroughly, answer Key posted on Canvas 5. Suppose you are interested in measuring the amount of time on average it takes you to make your commute to school. Over 18 random days, you estimated that the average time is 38.4 minutes with a standard deviation of 5.362 minutes. Construct a 90% confidence interval for the mean commute time to school.

6. For a random sample sample of size 12, one has calculated the 95% confidence interval for µ and obtained the result (46.2, 56.9). a) What is the margin of error for this confidence interval? b) What is the point estimate for that sample? c) Find the standard deviation (s) for that sample.

7. A random sample of 18 women is taken and their heights were recorded. The heights (in inches) are: 60, 62, 63, 63, 63, 66, 66, 66, 66, 67, 67, 68, 68, 68, 69, 70, 71, 71 Assume that women’s height are normally distributed. Let µ be the mean height of all women and let p be the proportion of all women that are taller than 65 inches. Use alpha=5%. a) Test the hypothesis H 0 : µ = 65 against H 1 : µ > 65. Find the test statistic and report your conclusion. b) Test the hypothesis H 0 : p = 0.5 against H 1 : p > 0.5. Find the test statistic and report your conclusion.

8. A forester measured 20 of the trees in a large woods that is up for sale. He found that their mean diameter was 191 inches and their standard deviation 22.4 inches. Suppose that these trees provide an accurate description of the whole forest and that the diameter of the tree follows a normal distribution. Find the following: a) What percentage of trees would be above 191 inches in diameter? b) What percentage of trees would be between 180 and 190 inches? c) What size diameter would you say represents the top 20% of the trees?

9. Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 395 elementary school teachers and 266 high school teachers. Of the elementary school teachers, 224 said they were very satisfied with their jobs, whereas 126 of the high school teachers were very satisfied with their work. Use alpha=5%. a) Estimate the difference between the proportion of all elementary school teachers who are very satisfied and all high school teachers who are very satisfied by calculating and interpreting a confidence interval (CI). b) Perform an appropriate statistical test to this problem and compare your answer to part(a).

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