Elementary Statistics: A Step-by-Step Approach with Formula Card
Elementary Statistics: A Step-by-Step Approach with Formula Card
9th Edition
ISBN: 9780078136337
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 9, Problem 16CQ

a.

To determine

To identify: The claim and state H0 and Ha

a.

Expert Solution
Check Mark

Answer to Problem 16CQ

The claim is that “there is a significant difference in price”.

The hypotheses are given below:

Null hypothesis: H0:μ1=μ2

Alternative hypothesis: H1:μ1μ2 (claim)

Explanation of Solution

Given info:

x¯1=1.43 , x¯2=1.03 , s1=0.09 , s2=0.10 , n1=12 , and n2=16

Justification:

Here, there is a significant difference in prices tested. Hence, the claim is that there is a significant difference in price. This can be written as μ1μ2 . The complement of the claim is μ1=μ2 . In the given experiment, the alternative hypothesis indicates the claim.

The hypotheses are given below:

Null hypothesis:

H0:μ1=μ2

Alternative hypothesis:

H1:μ1μ2

b.

To determine

To find: The critical value α=0.01 .

b.

Expert Solution
Check Mark

Answer to Problem 16CQ

The critical value at α=0.01 is ±3.106 .

Explanation of Solution

Calculation:

Here, the test is two tailed test.

Critical value:

Here, variances are not equal. Hence, the degrees of freedom is,

df=Smallar of n11 and  n21=121=11

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘t’ distribution.
  • In Degrees of freedom, enter 11.
  • Click the Shaded Area tab.
  • Choose Probability value and Two Tail for the region of the curve to shade.
  • Enter the Probability value as 0.01.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step-by-Step Approach with Formula Card, Chapter 9, Problem 16CQ , additional homework tip  1

From the output, the critical value is ±3.106 .

c.

To determine

To find: The test value.

c.

Expert Solution
Check Mark

Answer to Problem 16CQ

The test value is 11.09.

Explanation of Solution

Calculation:

Test statistic:

Software Procedure:

Step by step procedure to obtain test statistic using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Summarized data.
  • In first, enter Sample size as 12, Mean as 1.43, Standard deviation as 0.09.
  • In second, enter Sample size as 16, Mean as 1.03, Standard deviation as 0.1.
  • Choose Options.
  • In Confidence level, enter 99.
  • In Alternative, select not equal.
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Elementary Statistics: A Step-by-Step Approach with Formula Card, Chapter 9, Problem 16CQ , additional homework tip  2

From the MINITAB output, the test value is 11.09.

d.

To determine

To make: The decision.

d.

Expert Solution
Check Mark

Answer to Problem 16CQ

The decision is that, the null hypothesis isrejected.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to indicate the appropriate area and critical value using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘t’ distribution.
  • In Degrees of freedom, enter 11.
  • Click the Shaded Area tab.
  • Choose Probability value and Two Tail for the region of the curve to shade.
  • Enter the Probability value as 0.01.
  • Enter 11.09 under show reference lines at X values
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step-by-Step Approach with Formula Card, Chapter 9, Problem 16CQ , additional homework tip  3

From the output, it can be observed that the test statistic value falls in the critical region. Therefore, the null hypothesis isrejected.

e.

To determine

To summarize: The result.

To construct: The 99% confidence interval for the difference of the mean.

e.

Expert Solution
Check Mark

Answer to Problem 16CQ

The conclusion is that, there is enough evidence to support the claim that there is a significant difference in price.

The 99% confidence interval for the difference of the mean is (0.2995,0.5005) .

Explanation of Solution

Justification:

From part (d), the null hypothesis is rejected. Thus, there is enough evidence to support the claim that there is a significant difference in price.

Confidence interval:

From the MINITAB output in part (c), the 99% confidence interval for the difference of the mean is (0.2995,0.5005) .

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Chapter 9 Solutions

Elementary Statistics: A Step-by-Step Approach with Formula Card

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