Concept explainers
(a)
To find: The pooled probability of success for the two experiments.
(a)
Answer to Problem 5P
Solution: The pooled probability of success is
Explanation of Solution
Calculation: Using,
Now, the pooled probability of success is calculated as follows:
Thus, the probability of success is 0.66.
Now the value of the
Thus, the probability of failure is 0.34.
(b)
Whether we should use
(b)
Answer to Problem 5P
Solution: The sample test statistic follows standard normal distribution.
Explanation of Solution
The number of binomial trials is large enough that each of the products
(c)
The null and alternate hypothesis.
(c)
Answer to Problem 5P
Solution: The hypotheses are
Explanation of Solution
Since, we want to conduct a test of the claim that the probability of success of the two binomial experiments are differ. Therefore, the null hypothesis is
(d)
To find: The difference of sample proportion
(d)
Answer to Problem 5P
Solution: The difference of sample proportion
Explanation of Solution
Calculation:
The difference of
Thus, thedifference of sample proportion
The sample test statistic is calculated as follows:
Thus, the sample test statistic is -1.42.
(e)
To find: The P-value of the sample test statistic.
(e)
Answer to Problem 5P
Solution: The P-value of test statistic is approximately 0.1556.
Explanation of Solution
Calculation:
The P-value is calculated as follows:
Using table 3 from Appendix, we get
Thus the P-value of the sample test statistic is approximately 0.1556.
(f)
Whether we should reject or fail to reject the null hypothesis for a 5% level of significance.
(f)
Answer to Problem 5P
Solution: The
Explanation of Solution
The P-value is greater than the level of significance (
(g)
Interpretation for the result.
(g)
Answer to Problem 5P
Solution: We have insufficient evidence in the favor of the claim the probability of success for the two binomial experiments are different from each other.
Explanation of Solution
The P-value is greater than the level of significance (
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Chapter 10 Solutions
EBK UNDERSTANDING BASIC STATISTICS
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