Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 7.1, Problem 10AYU
To determine
Whether the graph can represent a normal curve. If it cannot, explain the reason.
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Consider the state space model X₁ = §Xt−1 + Wt, Yt
=
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Є R4
and Y E R². Suppose we know the covariance matrices for Wt and Vt. How many
unknown parameters are there in the model?
Business Discuss
You want to obtain a sample to estimate the proportion of a population that possess a particular genetic marker. Based on previous evidence, you believe approximately p∗=11% of the population have the genetic marker. You would like to be 90% confident that your estimate is within 0.5% of the true population proportion. How large of a sample size is required?n = (Wrong: 10,603)
Do not round mid-calculation. However, you may use a critical value accurate to three decimal places.
Chapter 7 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 7.1 - A _____ _____ _____ is an equation used to compute...Ch. 7.1 - A _______ is an equation, table, or graph used to...Ch. 7.1 - True or False: The normal curve is symmetric about...Ch. 7.1 - The area under the normal curve to the right of ...Ch. 7.1 - The points at x = _____ and x = _____ are the...Ch. 7.1 - The area under a normal curve can be interpreted...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - Prob. 10AYU
Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Prob. 15AYUCh. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Uniform Distribution The random-number generator...Ch. 7.1 - Uniform Distribution The reaction time X (in...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - One graph in the figure on the following page...Ch. 7.1 - One graph in the figure below represents a normal...Ch. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - Prob. 27AYUCh. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - In Problems 29 and 30, draw a normal curve and...Ch. 7.1 - Prob. 30AYUCh. 7.1 - NW You Explain It! Cell Phone Rates Monthly...Ch. 7.1 - You Explain It! Refrigerators The lives of...Ch. 7.1 - You Explain It! Birth Weights The birth weights of...Ch. 7.1 - You Explain It! Height of 10-Year-Old Males The...Ch. 7.1 - NW You Explain It! Gestation Period The lengths of...Ch. 7.1 - Prob. 36AYUCh. 7.1 - Hitting with a Pitching Wedge In the game of golf,...Ch. 7.1 - Heights of Five-Year-Old Females The following...Ch. 7.1 - Cardiac Arrest Researchers conducted a prospective...Ch. 7.2 - A random variable Z that is normally distributed...Ch. 7.2 - The notation z is the z-score such that the area...Ch. 7.2 - If X is a normal random variable with mean 40 and...Ch. 7.2 - If X is normal random variable with mean 40 and...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1922, find the value of z. 19. NW...Ch. 7.2 - In Problems 1922, find the value of z. 20. z0.02Ch. 7.2 - In Problems 1922, find the value of z. 21. z0.025Ch. 7.2 - In Problems 1922, find the value of z. 22. z0.015Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - Egg Incubation Times The mean incubation time of...Ch. 7.2 - Reading Rates The reading speed of sixth-grade...Ch. 7.2 - NW Chips Ahoy! Cookies The number of chocolate...Ch. 7.2 - Wendys Drive-Through Fast-food restaurants spend...Ch. 7.2 - Gestation Period The lengths of human pregnancies...Ch. 7.2 - Light Bulbs General Electric manufactures a...Ch. 7.2 - Manufacturing Steel rods are manufactured with a...Ch. 7.2 - Manufacturing Ball bearings are manufactured with...Ch. 7.2 - NCAA Basketball Point Spreads In sports betting,...Ch. 7.2 - Prob. 46AYUCh. 7.2 - NW Egg Incubation Times The mean incubation time...Ch. 7.2 - Reading Rates The reading speed of sixth-grade...Ch. 7.2 - Chips Ahoy! Cookies The number of chocolate chips...Ch. 7.2 - Wendys Drive-Through Fast-food restaurants spend...Ch. 7.2 - Speedy Lube The time required for Speedy Lube to...Ch. 7.2 - Putting It Together: Birth Weights The following...Ch. 7.2 - Prob. 53AYUCh. 7.2 - Prob. 54AYUCh. 7.2 - Explain why P(X 220) should be reported as ...Ch. 7.2 - The ACT and SAT are two college entrance exams....Ch. 7.3 - A _____ _____ _____ is a graph that plots observed...Ch. 7.3 - True or False: A normal score is the expected...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - Chips per Bag In a 1998 advertising campaign,...Ch. 7.3 - Hours of TV A random sample of college students...Ch. 7.3 - Putting It Together: Demon Roller Coaster Retrieve...Ch. 7.4 - In a binomial experiment with n trials and...Ch. 7.4 - When adding or subtracting 0.5 from X, we are...Ch. 7.4 - Suppose X is a binomial random variable. To...Ch. 7.4 - Suppose X is a binomial random variable. To...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 9AYUCh. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 11AYUCh. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 13AYUCh. 7.4 - Prob. 14AYUCh. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - Prob. 19AYUCh. 7.4 - Prob. 20AYUCh. 7.4 - NW On-Time Flights According to American Airlines,...Ch. 7.4 - Prob. 22AYUCh. 7.4 - Prob. 23AYUCh. 7.4 - Sneeze According to a study done by Nick Wilson of...Ch. 7.4 - Males Living at Home According to the Current...Ch. 7.4 - Females Living at Home According to the Current...Ch. 7.4 - NW Boys Are Preferred In a Gallup poll, 37% of...Ch. 7.4 - Liars According to a USA Today Snapshot, 3% of...Ch. 7 - Use the figure to answer the questions that...Ch. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - Find the z-score such that the area to the right...Ch. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Tire Wear Suppose that Dunlop Tire manufactures a...Ch. 7 - Wechsler Intelligence Scale The Wechsler...Ch. 7 - Major League Baseballs According to Major League...Ch. 7 - America Reads According to a Gallup poll, 46% of...Ch. 7 - Prob. 14RECh. 7 - Hector obtained a random sample of twenty recent...Ch. 7 - Density of Earth In 1798, Henry Cavendish obtained...Ch. 7 - Creative Thinking According to a USA Today...Ch. 7 - A continuous random variable X is uniformly...Ch. 7 - List the properties of the normal density curve.Ch. 7 - Prob. 20RECh. 7 - Prob. 1CTCh. 7 - Prob. 2CTCh. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Suppose that the talk time on the Apple iPhone is...Ch. 7 - The waist circumference of males 2029 years old is...Ch. 7 - Suppose the scores earned on Professor McArthurs...Ch. 7 - In a poll conducted by the Gallup organization,...Ch. 7 - Prob. 10CTCh. 7 - A continuous random variable X is uniformly...Ch. 7 - The reference interval for HDL cholesterol is...
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- 2. [20] Let {X1,..., Xn} be a random sample from Ber(p), where p = (0, 1). Consider two estimators of the parameter p: 1 p=X_and_p= n+2 (x+1). For each of p and p, find the bias and MSE.arrow_forward1. [20] The joint PDF of RVs X and Y is given by xe-(z+y), r>0, y > 0, fx,y(x, y) = 0, otherwise. (a) Find P(0X≤1, 1arrow_forward4. [20] Let {X1,..., X} be a random sample from a continuous distribution with PDF f(x; 0) = { Axe 5 0, x > 0, otherwise. where > 0 is an unknown parameter. Let {x1,...,xn} be an observed sample. (a) Find the value of c in the PDF. (b) Find the likelihood function of 0. (c) Find the MLE, Ô, of 0. (d) Find the bias and MSE of 0.arrow_forward3. [20] Let {X1,..., Xn} be a random sample from a binomial distribution Bin(30, p), where p (0, 1) is unknown. Let {x1,...,xn} be an observed sample. (a) Find the likelihood function of p. (b) Find the MLE, p, of p. (c) Find the bias and MSE of p.arrow_forwardGiven the sample space: ΩΞ = {a,b,c,d,e,f} and events: {a,b,e,f} A = {a, b, c, d}, B = {c, d, e, f}, and C = {a, b, e, f} For parts a-c: determine the outcomes in each of the provided sets. Use proper set notation. a. (ACB) C (AN (BUC) C) U (AN (BUC)) AC UBC UCC b. C. d. If the outcomes in 2 are equally likely, calculate P(AN BNC).arrow_forwardSuppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values for normal probability plots. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0.191 0.186 0.201 0.2005 0.203 0.210 0.234 0.248 0.260 0.273 0.281 0.290 0.305 0.310 0.308 0.311 Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) ○ A. Yes. The correlation between the expected z-scores and the observed data, , exceeds the critical value, . Therefore, it is reasonable to conclude that the data come from a normal population. ○…arrow_forwardding question ypothesis at a=0.01 and at a = 37. Consider the following hypotheses: 20 Ho: μ=12 HA: μ12 Find the p-value for this hypothesis test based on the following sample information. a. x=11; s= 3.2; n = 36 b. x = 13; s=3.2; n = 36 C. c. d. x = 11; s= 2.8; n=36 x = 11; s= 2.8; n = 49arrow_forward13. A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Would the manager of the pharmaceutical company be more concerned about a Type I error or a Type II error? Explain.arrow_forwardFind the z score that corresponds to the given area 30% below z.arrow_forwardFind the following probability P(z<-.24)arrow_forward3. Explain why the following statements are not correct. a. "With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error." b. "I have already decided how much of the Type I error I am going to allow. A bigger sample will not change either the Type I or Type II error." C. "I can reduce the Type II error by making it difficult to reject the null hypothesis." d. "By making it easy to reject the null hypothesis, I am reducing the Type I error."arrow_forwardGiven the following sample data values: 7, 12, 15, 9, 15, 13, 12, 10, 18,12 Find the following: a) Σ x= b) x² = c) x = n d) Median = e) Midrange x = (Enter a whole number) (Enter a whole number) (use one decimal place accuracy) (use one decimal place accuracy) (use one decimal place accuracy) f) the range= g) the variance, s² (Enter a whole number) f) Standard Deviation, s = (use one decimal place accuracy) Use the formula s² ·Σx² -(x)² n(n-1) nΣ x²-(x)² 2 Use the formula s = n(n-1) (use one decimal place accuracy)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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