a.
To identify: The claim and state
a.
Answer to Problem 18CQ
The claim is that “there is a significant difference between the two states in chemists’ salaries”.
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
Justification:
Here, there is a significant difference between the two states in chemists’ salaries is tested. Hence, the claim is that there is a significant difference between the two states in chemists’ salaries. This can be written as
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
b.
To find: The critical value
b.
Answer to Problem 18CQ
The critical value at
Explanation of Solution
Calculation:
Here, the test is two tailed test.
Critical value:
Here, variances are not equal. Hence, the degrees of freedom is,
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 0.02.
- Click OK.
Output using the MINITAB software is given below:
From the output, the critical value is
c.
To find: The test value.
c.
Answer to Problem 18CQ
The test value is 9.81.
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 39,420, Standard deviation as 1,659. - In second, enter Sample size as26, Mean as 30,215, Standard deviation as 4,116.
- Choose Options.
- In Confidence level, enter 98.
- In Alternative, select not equal.
- Click OK in all the dialogue boxes.
Output using the MINITAB software is given below:
From the MINITAB output, the test value is 9.81.
d.
To make: The decision.
d.
Answer to Problem 18CQ
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 0.02.
- Enter 9.81 under show reference lines at X values
- Click OK.
Output using the MINITAB software is given below:
From the output, it can be observed that the test statistic value falls in the critical region. Therefore, the null hypothesis isrejected.
e.
To summarize: The result.
To construct: The 99% confidence interval for the difference of the mean.
e.
Answer to Problem 18CQ
The conclusion is that, there is enough evidence to support the claim that there is a significant difference between the two states in chemists’ salaries.
The 98% confidence interval for the difference of the mean is
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 between the two states in chemists’ salaries.
Confidence interval:
From the MINITAB output in part (c), the 98% confidence interval for the difference of the mean is
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Chapter 9 Solutions
ALEKS 360 ELEM STATISTICS
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- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill