Concept explainers
a.
Find the value of t-test statistic.
a.
Answer to Problem 4CYU
The value of t-test statistic is 1.651768.
Explanation of Solution
Calculation:
The given statistics for testing the hypothesis
Requirements for a small sample t-test:
- The samples must be independent and drawn randomly from the populations.
- Either the sample size must be greater than 30 or the population must be approximately normal.
Here, it is given that independent random samples are drawn from approximately normal populations.
Thus, the conditions are satisfied.
The hypotheses are given below:
Null hypothesis:
Alternate hypothesis:
The test statistic for the small sample t is obtained as follows:
Under the null hypothesis,
Therefore the test statistic is,
Thus, the test statistic is 1.651768.
b.
Find the number of degrees of freedom for the test statistic.
b.
Answer to Problem 4CYU
The number of degrees of freedom for the test statistic is 16.
Explanation of Solution
Calculation:
Degrees of freedom:
The degrees of freedom for t using computer package is,
The degrees of freedom, when computing by hand is smaller of
The degrees of freedom is,
Thus, the degree of freedom is 16.
c.
Find the P-value.
c.
Answer to Problem 4CYU
The P-value is 0.11806.
Explanation of Solution
Calculation:
P-value:
Step-by-step procedure to obtain the P-value using the MINITAB software:
- Choose Graph > Probability Distribution Plot.
- Choose View Probability > OK.
- From Distribution, choose‘t’ distribution.
- In Degrees of freedom, enter 16.
- Click the Shaded Area tab.
- Choose X value and Both Tail for the region of the curve to shade.
- In X-value enter 1.651768.
- Click OK.
Output using the MINITAB software is given below:
From the MINITAB output, the P-value is
Thus, the P-value is 0.11806.
d.
Interpret the P-value.
Check whether the null hypothesis is rejected at
d.
Answer to Problem 4CYU
There is not enough evidence to reject the null hypothesis at
Explanation of Solution
Decision rule based on P-value:
If
If
Here, the level of significance is
Conclusion based on P-value approach:
The P-value is 0.11806 and
Here, P-value is greater than the
That is
By the rejection rule, failed to reject the null hypothesis.
Hence, the null hypothesis cannot be rejected at
Thus, it can be concluded that there is sufficient evidence to infer the equality of two population means at
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Chapter 9 Solutions
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