2. For a population of N = 10 scores, you first measure the distance.pdf

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2. Find the equation of the parabola that satisfied the following conditions.Vertex (0,0), latus rectum = 16, opens to the right. Solution Latus rectum for standard parabola = |4a| Hence |a| for the given parabola = 4 As vertex is at (0,0) and the parabola open to the right focus is (4,0) The standard equation is y² = 4ax. The equation of the given parabola = y² = 4*4x = 16x.

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2. For a population of N = 10 scores, you first measure the distance between each score and the
mean, then square each distance and find the sum of the squared distances. What value have you
calculated? a. SS b.the population variance c.the population standard deviation d.none of the
above 3. What are the values for SS and variance for the following sample of n = 3 scores?
Sample: 1, 4, 7 a.SS = 18 and variance = 6 b.SS = 18 and variance = 6 c.SS = 66 and variance
= 22 d.SS = 66 and variance 33 4. What is the variance for the following population of scores?
Scores: 5, 2, 5, 4 a.6 b.2 c.1.5 d.1.22 5.What term is used to identify the standard deviation
of the distribution of sample means? a.the expected value of M b.the standard error of M c.the
sample mean d.the central limit mean 6.A sample of n = 25 scores is selected from a
population with ? = 100 with ? = 20. On average, how much error would be expected between
the sample mean and the population mean? a.25 points b.20 points c.4 points d.0.8 points
Solution
2. b. the population variance 3. b. SS = 18 and variance = 6 4.b. 2 5. b. the standard
error of M c. 6. c. 4 points

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HW1_STAT206.pdf Statistical Inference II: J. Lee Assignment 1 Problem 1. Suppose the day after the Drexel-Northeastern basketball game, a poll of 1000 Drexel students was conducted and it was determined that 850 out of the 1000 watched the game (live or on television). Assume that this was a simple random sample and that the Drexel undergraduate population is 20000. (a) Generate an unbiased estimate of the true proportion of Drexel undergraduate students who watched the game. (b) What is your estimated standard error for the proportion estimate in (a)? (c) Give a 95% confidence interval for the true proportion of Drexel undergraduate students who watched the game. Problem 2. (Exercise 18 in Chapter 7 of Rice) From independent surveys of two populations, 90% confidence intervals for the population means are conducted. What is the probability that neither interval contains the respective population mean? That both do? Problem 3. (Exercise 23 in Chapter 7 of Rice) (a) Show that the standard error of an estimated proportion is largest when p = 1/2. (b) Use this result and Corollary B of Section 7.3.2 (also, on Page 17 of the lecture notes) to conclude that the quantity 1 2 √ N − n N(n − 1) is a conservative estimate of the standard error of p̂ no matter what the value of p may be. (c) Use the central limit theorem to conclude that the interval p̂ ± √ N − n N(n − 1) contains p with probability at least .95. HW2_STAT206.pdf Statistical Inference II: J. Lee Assignment 2 Problem 1. The following data set represents the number of NBA games in January 2016, watched by 10 randomly selected student in STAT 206. 7, 0, 4, 2, 2, 1, 0, 1, 2, 3 (a) What is the sample mean? (b) Calculate sample variance. (c) Estimate the mean number of NBA games watched by a student in January 2016. (d) Estimate the standard error of the estimated mean. Problem 2. True or false? Tell me why for the false statements. (a) The center of a 95% confidence interval for the population mean is a random variable. (b) A 95% confidence interval for µ contains the sample mean with probability .95. (c) A 95% confidence interval contains 95% of the population. (d) Out of one hundred 95% confidence intervals for µ, 95 will contain µ. Problem 3. An investigator quantifies her uncertainty about the estimate of a population mean by reporting X ± sX . What size confidence interval is? Problem 4. For a random sample of size n from a population of size N, consider the following as an estimate of µ: Xc = n∑ i=1 ciXi, where the ci are fixed numbers and X1, . . . ,Xn are the sample. Find a condition on the ci such that the estimate is unbiased. Problem 5. A sample of size 100 has the sample mean X = 10. Suppose the we know that the population standard deviation σ = 5. Find a 95% confidence interval for the population mean µ. Problem 6. Suppose the we know that the population standard deviation σ = 5. Then how large should a sample be to estimate the popula.

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Assignment #9 First, we recall some definitions that will be helpful in answering questions 1-3 A population parameter is a single value that describes a population characteristic (such as center, spread, location etc.) EXAMPLES: · The proportion p of adults in the United States who worry about money · The mean lifetime m of a certain brand of computer hard disks · The lower quartile 1 q of a population of incomes · The standard deviation s of the nicotine content per cigarette produced by a certain manufacture. In real life, population parameters are usually unknown. An important objective of statistical inference is to use information obtained from random sample or samples (depending on the design of the study) to estimate parameters and to test claims made about them. A statistic is a number computed form the sample data only. The resulting sample value must be independent of the population parameters. Statistics are used as numerical estimates of population parameters. Example: A random sample of 1500 national adults shows that 33% of Americans worry about money. The margin of error is +/- 3 percentage points. Statistics have variation. Different random samples of size n from the same population will usually yield different values of the same statistic. This is called sampling variability. The sampling distribution of a statistic is the distribution of the values taken by the statistic over all possible random samples of the same size from a given population. What do we look for in a sampling distrinution? Bias: A statistic is unbiased if its sampling distribution has a mean that is equal to the true value of the parameter being estimated by that statistic. Variability: How much variation is there in the sampling distribution? The goal of this assignment is to simulate the sampling distribution of some statistics. Question 1: An urn contains 50 beads. The beads are identical in shape and have one of two colors: blue and orange. We would like to estimate the proportion p of blue beads. We select without replacement a sample of 10 beads. The relevant statistics is the sample proportion p ˆ of blue beads (i.e., the number of blue beads in the sample divided by 10. For the purpose of the simulation exercise, we will assume that the box contains exactly 15 blue beads or, equivalently, the proportion of blue beads is 30 . 0 = p . i) Select 100 samples of size 10 from the box. ii) Compute the sample proportion p ˆ of blue beads for each of the 100 samples found in (i). iii) Make a histogram of the values of p ˆ found in (ii) (that is the approximate sampling distribution of p ˆ .) iv) Find the summary statistics of the 100 values of p ˆ . v) Base yourself on the histogram and the summary statistics to describe the approximate sampling distribution of p ˆ . vi) Is p ˆ an unbiased estimator of p ? Hint: Evaluate the difference between 30 . 0 = p and the mean value. ...

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