#8. Using Minitab to illustrate the Central Limit Theorem (CLT), the CLT tells us about thesampling distribution of the sample mean. With Minitab we can easily "sample" from apopulation with known properties (4,0 , shape).a. Our population consists of integer values X from 1 through 8, all equally likelyР(x) 3D 1/8; х %3D1, 2, 3, 4, 5, 6, 7, 8Using methods from the beginning of Chapter 4 in the textbook, find u.Use your calculator to find u. What is the shape of this probability distribution? Does ito =2.29"look" Normal?b. Take a sample of size 3 from this population and compute the sample mean. Repeat thisprocess 1000 times.Click on Calc > Random DataRows 1000Store in columns C1-C3Distribution IntegerMinimum 1Maximum 8Compute the mean of each sample (row) and store the sample means in C4.Note: C4 has 1000 sample means each a sample of size n=3.Click on Calc → Row StatisticsO MeanInput Variables C1-C3Store C4 c. Compute the mean and stand. dev. of your 1000 sample means.Click on Stat = Basic Statistics = Display Descriptive StatisticsVariable C4Statistics check only mean and standard deviationWhat did you expect for the mean of the sample means?What did you get?What did you expect for the stand. dev. of the sample means?What did you get?Briefly explain, how this illustrates 2 parts of the CLT.d. Draw a histogram of your sample means.Click on Graph Histogram SimpleGraph Variable C4Discuss how this graph illustrates the CLT.(Note: For #8 the sample size n=3 is less than 30)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Let Y₁ 10). Hint: See example 6-3.2 in the book.
• Let X; denote the rate for the ith state in 2005. • Let Y; denote the rate for the ith state in 2015. • Let D; = Y; – X; denote the difference in rates for the ith state. • Let S3, S?, S denote the sample variances and X,Ÿ,D denote the sample means. • Let 0x,0y denote the nationwide mean mortality rates in 2005 and 2015. • Let Op = 0y – 0x. 1. Answer the following questions using the differences D1,..., D20 shown in Figure 2. (a) Test the hypothesis that the mean U.S. mortality rate 0p remained the same or increased from 2005 to 2015 against the alternative that the mean mortality rate decreased. State the hypotheses, test statistic, rejection region, and p-value. Interpret the conclusion of the test at level a = 0.01. (b) Calculate the power of the test you performed in the previous part at OD = -10. What is the type II error rate for this alternative scenario? (c) Compute a 99% confidence interval for the change in mean heart rate mortality. Interpret the interval in context. (d)…
A two-factor, independent-samples design is evaluated using an analysis of variance. The F-ratio for factor A has df = (2, 99) and the F-ratio for factor B has df = (2, 99). Based on this information, the degrees of freedom for A x B interaction would be df = (censored, ____________). Fill in the blank for the second value.
The following information is available for two samples selected from independent normally distributed populations. Population A: n1=30 S2/1=36 Population B: n2=30 S2/2= 25 What is the value of FSTAT? FSTAT=________ (Round to two decimal places as needed.)
The following table shows crashworthiness ratings for 16 cars. (3 = Good, 2 = Acceptable, 1 = Marginal, 0 = Poor) Frontal Crash Test Rating 3 2 1 0 Frequency 1 11 2 2 (a) Find the relative frequency distribution for the experiment of choosing a car at random and determining its frontal crash rating. (Enter your answers to four decimal places.) Good (3) Acceptable (2) Marginal (1) Poor (0) (b) What is the relative frequency that a randomly selected car will have a crash test rating of "Marginal" or worse? (Enter your answer to four decimal places.)
Excel Inferences of population variance(s): Buyer’s Digest CaseBuyer’s Digest rates thermostats manufactured for home temperature control. In arecent test, 10 thermostats manufactured by ThermoRite were randomly selected andplaced in a test room that was maintained at a temperature of 68oF. The temperaturereadings of the ten thermostats are shown below:Thermostat 1 2 3 4 5 6 7 8 9 10Temperature 67.4 67.8 68.2 69.3 69.5 67.0 68.1 68.6 67.9 67.2 Buyer’s Digest gives an “acceptable” rating to a thermostat with a temperature variance of 0.5 or less. Given significance level of α = 0.05, use a formal hypothesis test to determine whether the ThermoRite products are “acceptable” in the quality measured in the variance. r the ThermoRite’s claim is valid.
5. Suppose monthly starting salaries for new college graduates in economics follow a normal distribution with mean of $5500 and standard deviation of $2000 and you are interested in estimating the population mean of $5500 based on a survey of n graduates. Conduct the following simulations to see the sampling distribution of X = X X₁/n, where X; is a monthly starting salary of ith surveyee. (a) Generate n = 10 data following N(5500, 2000²) and calculate the sample average X. Repeat 100 times and draw a histogram of Xs, using using a class width of $200 with the first class at $4000 and the last class at $8000.
1
2.) The table shows the distribution of a random sample of fatal motor vehicle collisions by time of day and gender in a recent year. Use a = 0.10 significance to perform a Chi-Square hypothesis test. O: E: C: O: E: C: totals: 12:00-5:59 6:00-11:59 654 308 490 231 12:00-5:59 pm 654 308 6:00-11:59 pm 1471 692 totals
A2
4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)
Solve this question only for parts D, E and F.

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