Connect Hosted by ALEKS Access Card or Elementary Statistics
Connect Hosted by ALEKS Access Card or Elementary Statistics
3rd Edition
ISBN: 9781260373752
Author: William Navidi Prof., Barry Monk Professor
Publisher: McGraw-Hill Education
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Chapter 13.2, Problem 7E

a.

To determine

To construct:a 95% confidence interval for mean response when x=2

a.

Expert Solution
Check Mark

Answer to Problem 7E

  7.89±1.5431738

Explanation of Solution

Given information: the sample size 25 , b0=3.25,b1=2.32,se=3.53,(xx¯)2=224.05,x¯=0.98

Formula Used:the formulas to be used when constructing a confidence interval for a mean response and when constructing a prediction interval for an individual response.

Let x* be a value of the explanatory variable x , let y=b0+b1x* be the predicted value corresponding to x* and let n be the sample size .A level 100(1α)% prediction interval for the mean response is

  y±tα/2.se1n+ ( x * x ¯ )2 (x x ¯ ) 2

Here, the critical value tα/2 is based on n2 degrees of freedom.

Let x* be a value of the explanatory variable x , let y=b0+b1x* be the predicted value corresponding to x* and let n be the sample size .A level 100(1α)% prediction interval for an individual response is

  y±tα/2.se1+1n+ ( x * x ¯ )2 (x x ¯ ) 2

Here, the critical value tα/2 is based on n2 degrees of freedom.

the predicted value corresponding to x* when x=2

  y=b0+b1x*y=3.25+2.32(2)y=3.25+4.64y=7.89

The t table corresponding t-value for the given confidence interval 95% and degrees of freedom 23 is not provided in the book. But below shows that the t-valueis 2.069 .

  Connect Hosted by ALEKS Access Card or Elementary Statistics, Chapter 13.2, Problem 7E , additional homework tip  1

Now to construct prediction interval for the mean response.

  y±tα/2.se1n+ ( x * x ¯ ) 2 (x x ¯ ) 2 7.89±tα/23.531 25+ (20.98) 2 224.057.89±tα/23.531 25+ (1.02) 2 224.057.89±tα/23.531 25+ 1.0404 224.057.89±tα/23.530.04+ 1.0404 224.057.89±tα/23.530.04+0.004643606337.89±tα/23.530.044643606337.89±tα/23.53(0.21129033659)7.89±tα/20.74585488817

  7.89±tα/20.745854888177.89±(2.069)(0.74585488817)7.89±1.5431738

b.

To determine

To construct: a 95% prediction interval for individual response when x=2

b.

Expert Solution
Check Mark

Answer to Problem 7E

  7.89±7.4648188

Explanation of Solution

Given information: the sample size 25 , b0=3.25,b1=2.32,se=3.53,(xx¯)2=224.05,x¯=0.98

Formula Used:the formulas to be used when constructing a confidence interval for a mean response and when constructing a prediction interval for an individual response.

Let x* be a value of the explanatory variable x , let y=b0+b1x* be the predicted value corresponding to x* and let n be the sample size .A level 100(1α)% prediction interval for the mean response is

  y±tα/2.se1n+ ( x * x ¯ )2 (x x ¯ ) 2

Here, the critical value tα/2 is based on n2 degrees of freedom.

Let x* be a value of the explanatory variable x , let y=b0+b1x* be the predicted value corresponding to x* and let n be the sample size .A level 100(1α)% prediction interval for an individual response is

  y±tα/2.se1+1n+ ( x * x ¯ )2 (x x ¯ ) 2

Here, the critical value tα/2 is based on n2 degrees of freedom.

the predicted value corresponding to x* when x=2

  y=b0+b1x*y=3.25+2.32(2)y=3.25+4.64y=7.89

The t table corresponding t-value for the given confidence interval 95% and degrees of freedom 23 is not provided.But below shows that the t-value is 2.069 .

  Connect Hosted by ALEKS Access Card or Elementary Statistics, Chapter 13.2, Problem 7E , additional homework tip  2

Now to construct prediction interval for the individual response.

  y±tα/2.se1n+ ( x * x ¯ ) 2 (x x ¯ ) 2 y±tα/2.se1+1n+ ( x * x ¯ ) 2 (x x ¯ ) 2 7.89±tα/23.531+1 25+ (20.98) 2 224.057.89±tα/23.531+0.04+ 1.0404 224.057.89±tα/23.531+0.04+ 1.0404 224.057.89±tα/23.531.044643606347.89±tα/23.53(1.02207808231)7.89±tα/23.60793563055

  7.89±tα/23.607935630557.89±(2.069)(3.60793563055)7.89±7.4648188

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Chapter 13 Solutions

Connect Hosted by ALEKS Access Card or Elementary Statistics

Ch. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 26aECh. 13.1 - Calculator display: The following TI-84 Plus...Ch. 13.1 - Prob. 28aECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - Confidence interval for the conditional mean: In...Ch. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Dry up: Use the data in Exercise 26 in Section...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - In Exercises 9 and 10, determine whether the...Ch. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - For the following data set: Construct the multiple...Ch. 13.3 - Engine emissions: In a laboratory test of a new...Ch. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13 - A confidence interval for 1 is to be constructed...Ch. 13 - A confidence interval for a mean response and a...Ch. 13 - Prob. 3CQCh. 13 - Prob. 4CQCh. 13 - Prob. 5CQCh. 13 - Prob. 6CQCh. 13 - Construct a 95% confidence interval for 1.Ch. 13 - Prob. 8CQCh. 13 - Prob. 9CQCh. 13 - Prob. 10CQCh. 13 - Prob. 11CQCh. 13 - Prob. 12CQCh. 13 - Prob. 13CQCh. 13 - Prob. 14CQCh. 13 - Prob. 15CQCh. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Air pollution: Following are measurements of...Ch. 13 - Icy lakes: Following are data on maximum ice...Ch. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 1WAICh. 13 - Prob. 2WAICh. 13 - Prob. 1CSCh. 13 - Prob. 2CSCh. 13 - Prob. 3CSCh. 13 - Prob. 4CSCh. 13 - Prob. 5CSCh. 13 - Prob. 6CSCh. 13 - Prob. 7CS
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