ALEKS 360 ESSENT. STAT ACCESS CARD
2nd Edition
ISBN: 9781266836428
Author: Navidi
Publisher: MCG
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Chapter 7, Problem 9RE
High octane: Fifty measurements are taken of the octane rating for a particular type of gasoline. The sample
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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.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 7 Solutions
ALEKS 360 ESSENT. STAT ACCESS CARD
Ch. 7.1 - Prob. 1CYUCh. 7.1 - Prob. 2CYUCh. 7.1 - Prob. 3CYUCh. 7.1 - Prob. 4CYUCh. 7.1 - Prob. 5CYUCh. 7.1 - Prob. 6CYUCh. 7.1 - Prob. 7CYUCh. 7.1 - Prob. 8CYUCh. 7.1 - Prob. 9CYUCh. 7.1 - 10. Using the output in Exercise 9:
Find the...
Ch. 7.1 - Prob. 11CYUCh. 7.1 - 12. The researchers now plan to construct a 99%...Ch. 7.1 - Prob. 13CYUCh. 7.1 - 14. An IQ test is designed to have scores that...Ch. 7.1 - Prob. 15CYUCh. 7.1 - Prob. 16CYUCh. 7.1 - In Exercises 17–20, fill in each blank with the...Ch. 7.1 - In Exercises 17–20, fill in each blank with the...Ch. 7.1 - Prob. 19ECh. 7.1 - In Exercises 17–20, fill in each blank with the...Ch. 7.1 - In Exercises 21–24, determine whether the...Ch. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - In Exercises 25–28, find the critical value zα∕2...Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - In Exercises 29–32, find the levels of the...Ch. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - 36. A sample of size n = 64 is drawn from a...Ch. 7.1 - 37. A sample of size n = 10 is drawn from a normal...Ch. 7.1 - 38. A sample of size n = 80 is drawn from a normal...Ch. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - 43. SAT scores: A college admissions officer takes...Ch. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - 56. Different standard deviations: Martin and...Ch. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Interpret computer output: The following MINITAB...Ch. 7.1 - Interpret computer output: The following MINITAB...Ch. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.2 - Prob. 1CYUCh. 7.2 - Prob. 2CYUCh. 7.2 - 3. A potato chip company wants to evaluate the...Ch. 7.2 - Prob. 4CYUCh. 7.2 - Prob. 5CYUCh. 7.2 - Prob. 6CYUCh. 7.2 - Prob. 7ECh. 7.2 - In Exercises 7 and 8, fill in each blank with the...Ch. 7.2 - In Exercises 9 and 10, determine whether the...Ch. 7.2 - In Exercises 9 and 10, determine whether the...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - 14. A sample of size n = 22 is drawn from a normal...Ch. 7.2 - 15. A sample of size n = 12 is drawn from a normal...Ch. 7.2 - Prob. 16ECh. 7.2 - 17. A sample of size n = 15 has sample mean and...Ch. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - 23. Fake Twitter followers: Many celebrities and...Ch. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - 26. Sound it out: Phonics is an instructional...Ch. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Baby weights: Following are weights, in pounds, of...Ch. 7.2 - Eat your cereal: Boxes of cereal are labeled as...Ch. 7.2 - Prob. 31ECh. 7.2 - Mortgage rates: Following are interest rates...Ch. 7.2 - Prob. 33ECh. 7.2 - Big salary for the boss: Following is the total...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Sleeping outlier: A simple random sample of eight...Ch. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Interpret computer output: The following MINITAB...Ch. 7.2 - Prob. 47ECh. 7.3 - A simple random sample of 200 third-graders in a...Ch. 7.3 - Prob. 2CYUCh. 7.3 - A pollster is going to sample a number of voters...Ch. 7.3 - Prob. 4CYUCh. 7.3 - Prob. 5CYUCh. 7.3 - In a simple random sample of 15 seniors from a...Ch. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - In Exercises 11–14, find the point estimate, the...Ch. 7.3 - In Exercises 11–14, find the point estimate, the...Ch. 7.3 - Prob. 13ECh. 7.3 - In Exercises 11–14, find the point estimate, the...Ch. 7.3 - In Exercises 15–18, use the given data to...Ch. 7.3 - In Exercises 15–18, use the given data to...Ch. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Smart phone: Among 238 cell phone owners aged...Ch. 7.3 - Working at home: According to the U.S. Census...Ch. 7.3 - Sleep apnea: Sleep apnea is a disorder in which...Ch. 7.3 - Internet service: An Internet service provider...Ch. 7.3 - Volunteering: The General Social Survey recently...Ch. 7.3 - SAT scores: A college admissions officer sampled...Ch. 7.3 - WOW: In the computer game World of Warcraft, some...Ch. 7.3 - Contaminated water: In a sample of 42 water...Ch. 7.3 - Call me: A sociologist wants to construct a 95%...Ch. 7.3 - Reading proficiency: An educator wants to...Ch. 7.3 - Surgical complications: A medical researcher wants...Ch. 7.3 - Prob. 30ECh. 7.3 - Changing jobs: A sociologist sampled 200 people...Ch. 7.3 - Prob. 32ECh. 7.3 - Small sample: Eighteen concrete blocks were...Ch. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.4 - Prob. 1CYUCh. 7.4 - Prob. 2CYUCh. 7.4 - Prob. 3CYUCh. 7.4 - In Exercises 1–4, state which type of parameter is...Ch. 7.4 - Prob. 5ECh. 7.4 - In Exercises 5–10, state which type of parameter...Ch. 7.4 - In Exercises 5–10, state which type of parameter...Ch. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Credit card debt: In a survey of 1118 U.S. adults...Ch. 7.4 - Pneumonia: In a simple random sample of 1500...Ch. 7.4 - Prob. 16ECh. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - Prob. 10CQCh. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Build more parking? A survey is to be conducted in...Ch. 7 - Drill lifetime: A sample of 50 drills had a mean...Ch. 7 - Cost of environmental restoration: In a survey of...Ch. 7 - More repairs: A sample of six records for repairs...Ch. 7 - Automobile pollution: In a random sample of 85...Ch. 7 - Contaminated water: Polychlorinated biphenyls...Ch. 7 - Defective electronics: A simple random sample of...Ch. 7 - Prob. 8RECh. 7 - High octane: Fifty measurements are taken of the...Ch. 7 - Super Bowl: A simple random sample of 140...Ch. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Leaking tanks: Leakage from underground fuel tanks...Ch. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 1WAICh. 7 - What factors can you think of that may affect the...Ch. 7 - Prob. 3WAICh. 7 - Prob. 4WAICh. 7 - Prob. 5WAICh. 7 - When constructing a confidence interval for μ, how...Ch. 7 - Prob. 1CSCh. 7 - Prob. 2CSCh. 7 - Prob. 3CSCh. 7 - Repeat Exercises 1 and 2 for the Year 2 data. The...Ch. 7 - Prob. 5CS
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