Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.4, Problem 44E
Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in Exercise 15 of Section 12.2 resulted in ŷ = 7.592, sŶ = .179 when x = 40 and ŷ = 9.741, sŶ = .253 for x = 60.
- a. Explain why sŶ is larger when x = 60 than when x = 40.
- b. Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40.
- c. Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40.
- d. If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?
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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Preference
Male
Female
TOTAL
Prefers dogs
\[36\]
\[20\]
\[56\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
problem 1
Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal.
\[P\left(\text{prefers dogs}\right)=\]
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Preference
Male
Female
TOTAL
Prefers dogs
\[\blueD{36}\]
\[\blueD{20}\]
\[\blueE{56}\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.
Business discuss
You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model.
Interpret the…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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