Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Textbook Question
Chapter 6, Problem 85H
A NUMMI assembly Line, which has been operating since 1984, has built an average of 6.000 cars and trucks a week. Generally, 10% of the car’s were defective coming off the assembly line. Suppose we draw a random sample of n 100 cars. Let X represent the number of defective cars In the sample. ‘What can we say about X In regard to the
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
Chapter 6 Solutions
Introductory Statistics
Ch. 6 - What is the z-score of x, when x = 1 and...Ch. 6 - Fill In the blanks. Jerome averages 16 points a...Ch. 6 - Use the Information in Example 6.3 to answer the...Ch. 6 - In 2012, 1,664,479 students took the SAT exam. The...Ch. 6 - Suppose X has a normal distribution with mean 25...Ch. 6 - The scores on a college entrance exam have an...Ch. 6 - If the area to the left of x is 0.012, then what...Ch. 6 - The golf scores for a school team were normally...Ch. 6 - The golf scores for a school team were normally...Ch. 6 - Use the Information in Example 6.10 to answer the...
Ch. 6 - Two thousand students took an exam. The scores on...Ch. 6 - Using the information from Example 6.12, answer...Ch. 6 - A bottle of water contains 12.05 fluid ounces with...Ch. 6 - A normal distribution has a mean of 61 and a...Ch. 6 - X~N(1,2)=Ch. 6 - A company manufactures rubber balls. The mean...Ch. 6 - X~N(-4, 1) What is the median?Ch. 6 - X~N(3,5)=Ch. 6 - X~N(2,1)=Ch. 6 - What does a z-score measure?Ch. 6 - What does standardizing a normal distribution do...Ch. 6 - Is X ~N(0, 1) a standardized normal distribution?...Ch. 6 - What is the z-score of x = 12, if it is two...Ch. 6 - What is the z-score of x = 9, if it is 1.5...Ch. 6 - What is the z-score of x = —2, if it is 2.78...Ch. 6 - What is the z-score of x = 7, if it is 0.133...Ch. 6 - Suppose X~ N(2, 6). What value of x has a z-score...Ch. 6 - Suppose X~ N(8, 1). ‘What value of x has a z-score...Ch. 6 - Suppose X ~N(9, 5). What value of x has a z-score...Ch. 6 - Suppose X~ N(2, 3). That value of x has a z-score...Ch. 6 - Suppose X ~N(4, 2). What value of x is 1.5...Ch. 6 - Suppose X ~N(4, 2). What value of x is two...Ch. 6 - Suppose X ~N(8, 9). What value of x is 0.67...Ch. 6 - Suppose X ~N(—1, 2). What is the z-score of x = 2?Ch. 6 - Suppose X ~N( 12, 6). What is the z-score of x =...Ch. 6 - Suppose X ~N(9, 3). What is the z-score of x = 9?Ch. 6 - Suppose a normal distribution has a mean of six...Ch. 6 - In a normal distribution, x = 5 and z = —1.25....Ch. 6 - In a normal distribution, x = 3 and z = 0.67. This...Ch. 6 - In a normal distribution, x = —2 and z = 6. This...Ch. 6 - In a normal distribution, x = —5 and z = —3.14....Ch. 6 - In a normal distribution, x= 6 and z —1.7. This...Ch. 6 - About what percent of x values from a normal...Ch. 6 - About what percent of the x values from a normal...Ch. 6 - About what percent of x values lie between the...Ch. 6 - Suppose X N( 15, 3). Between what x values does...Ch. 6 - Suppose X~ N(—3, 1). Between what x values does...Ch. 6 - Suppose X ~N(—3, 1). Between what x values does...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - Use the following information to answer the next t...Ch. 6 - Use the following information to answer the next t...Ch. 6 - How would you represent the area to the left of...Ch. 6 - What is the area to the right of one? Figure 6.13Ch. 6 - Is P(x < 1) equal to P(x1) ? ‘by?Ch. 6 - How would you represent the area to the left of...Ch. 6 - What is the area to the right of three? Figure...Ch. 6 - If the area to the left of x in a normal...Ch. 6 - If the area to the tight of x in a normal...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - X~N(6, 2) Find the probability that x is between...Ch. 6 - X~N(—3, 4) Find the probability that x is between...Ch. 6 - X~N(4,5) Find the maxium of x in the bottom...Ch. 6 - Use the following information to answer the next...Ch. 6 - Find the probability that a CD player will last...Ch. 6 - Find the 70th percentile of the distribution for...Ch. 6 - Use the following information to answer the next r...Ch. 6 - Use the following information to answer the next r...Ch. 6 - The length of time to find it takes to find a...Ch. 6 - The heights of the 430 National Basketball...Ch. 6 - The systolic blood pressure (given In millimeters)...Ch. 6 - Kyle’s doctor told him that the z-score for his...Ch. 6 - Height and weight are two measurements used to...Ch. 6 - In 2005, 1,475,623 students heading to college...Ch. 6 - Use the following information (0 answer the next...Ch. 6 - Use the following information (0 answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - According to a study done by De Anza students, the...Ch. 6 - IQ is normally distributed with a mean of 100 and...Ch. 6 - The percent of fat calories that a person In...Ch. 6 - Suppose that the distance of fly balls hit to the...Ch. 6 - In China, four-ear-olds average three bows a day...Ch. 6 - In the 1992 presidential election, Alaska's 40...Ch. 6 - Suppose that the duration of a particular type of...Ch. 6 - Tern Vogel, an amateur motorcycle racer, averages...Ch. 6 - Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung...Ch. 6 - Suppose that Ricardo and Anita attend different...Ch. 6 - Table 6.4 shows a sample of the maximum capacity...Ch. 6 - An expert witness for a paternity lawsuit...Ch. 6 - A NUMMI assembly Line, which has been operating...Ch. 6 - We flip a coin 100 times (n = 100) and note that...Ch. 6 - A $1 scratch off lotto ticket will be a inner one...Ch. 6 - Facebook provides a variety of statistics on its...
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