Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.   x 69 66 63 65 76 76 y 54 53 51 43 47 45 ​ Verify that Se ≈ 4.739, a ≈ 67.050, b ≈ –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places. answer choices: The 90% confidence interval for β is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47.   The 90% confidence interval for β is from –1.065 to 0.539 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.07 and 0.54.   The 90% confidence interval for β is from –0.882 to 0.355 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.88 and 0.36.   The 90% confidence interval for β is from –1.023 to 0.496 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.02 and 0.50.   The 90% confidence interval for β is from –1.309 to 0.782 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.31 and 0.78.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
 

x 69 66 63 65 76 76
y 54 53 51 43 47 45

Verify that Se ≈ 4.739, a ≈ 67.050, b  –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places.

answer choices:
The 90% confidence interval for β is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47.
 
The 90% confidence interval for β is from –1.065 to 0.539 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.07 and 0.54.
 
The 90% confidence interval for β is from –0.882 to 0.355 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.88 and 0.36.
 
The 90% confidence interval for β is from –1.023 to 0.496 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.02 and 0.50.
 
The 90% confidence interval for β is from –1.309 to 0.782 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.31 and 0.78.
Expert Solution
Step 1

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season

Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. 

n=6

The excel steps for regression is obtained as-

The steps taken to obtain the simple linear regression to determine the amount of time spent on homework can be predicted by amount of sleep is given as follows: -

  • Enter the data in Excel spreadsheet [ x and y]
  • Go to data>Go to data analysis>Select regression>click OK.
  • Select Input Y Range>Select Input X Range>click Labels>click Ok

The output obtained is given as follows-

Regression Statistics          
Multiple R 0.331          
R Square 0.109          
Adjusted R Square -0.113          
Standard Error 4.739          
Observations 6          
             
ANOVA            
  df SS MS F Significance F  
Regression 1 11.01801329 11.018013 0.490696 0.522220859  
Residual 4 89.81532004 22.45383      
Total 5 100.8333333        
             
  Coefficients Standard Error t Stat P-value Lower 90.0% Upper 90.0%
Intercept 67.050 26.078 2.571 0.062 11.457 122.644
x -0.263 0.376 -0.700 0.522 -1.065 0.539

The table below shows the required calculation-

  x y x2 y2
  69 54 4761 2916
  66 53 4356 2809
  63 51 3969 2601
  65 43 4225 1849
  76 47 5776 2209
  76 45 5776 2025
Total 415 293 28863 14409

Thus,

se4.739a67.050b-0.263ix=415jy=293ix2=28863jy2=14409

is verified.

 

 

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Chi-squared Tests
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman