
Concept explainers
Basic Computation: Testing
(a) Compute the pooled probability of success for the two experiments.
(b) Check Requirements What distribution does the sample test statistic follow? Explain.
(c) State the hypotheses.
(d) Compute
(c) Find the P-value of the sample test statistic.
(f) Conclude the test.
(g) Interpret the results.
(a)

To find: The pooled probability of success for the two experiments.
Answer to Problem 6P
Solution: The pooled probability of success for the two experiments is
Explanation of Solution
Calculation: Using,
Now, the pooled probability of success is calculated as follows:
The pooled probability of success is 0.36.
Now the value of the
The pooled probability of failure is 0.64.
(b)

Whether we should use normal distribution or not.
Answer to Problem 6P
Solution: The sample distribution 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.
Answer to Problem 6P
Solution: The hypotheses are
Explanation of Solution
Since, we want to conduct a test of the claim that the probability of success for the second binomial experiment is greater than that for the first. Therefore the null hypothesis is
(d)

To find: The difference of sample proportion
Answer to Problem 6P
Solution: The difference of sample proportion
Explanation of Solution
Calculation:
The difference of
Thus, the difference of sample proportion
The sample test statistic is calculated as follows:
Thus, the sample test statistic is - 2.2
(e)

To find: The P-value of the sample test statistic.
Answer to Problem 6P
Solution: The P-value of test statistic is approximately 0.0134.
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 0.0134.
(f)

Whether we should reject or fail to reject the null hypothesis for a 5% level of significance.
Answer to Problem 6P
Solution: The
Explanation of Solution
The P-value is less than the level of significance (
(g)

Interpretation for the result.
Answer to Problem 6P
Solution: We have sufficient evidence in the favor of the claim that the probability of success for the second binomial is greater than that for the first.
Explanation of Solution
The P-value is less than the level of significance (
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