(a)
To find: the
(a)
Answer to Problem 15.32E
The probability that exactly 1 out of 77 cases yields a positive result is
Explanation of Solution
Given:
The poll stayed open for several weeks in October 2012. Of the 1290 vote cast, 864 were “yes” response.
Calculation:
To solve for the probability that exactly 1 out of 77 tests yield a statistically significant result, you will need to reach back to chapter 12 and model this as a binomial probability. Use the binomial probability equation
Here is the initial setup. Remember that the value for
Now add the information for the binomial coefficients
The probability that exactly 1 out of 77 cases yields a positive result is
Conclusion:
Therefore, the probability that exactly 1 out of 77 cases yields a positive result is
(b)
To prove: it is not surprising that 2 of the 77 tests were statistically significant at the 5% level.
(b)
Answer to Problem 15.32E
It is not surprising that 2 of the 77 tests yielded significant results.
Explanation of Solution
Calculation:
Because they ran 77 tests at a 5% significance level, then you would expect to see about 4 of these 77 tests have a significant result based on the following logic.
It is similar to rolling double 6's in craps. You expect this to occur 1 out of 36 times which means
It has a significance level of
Thus it is not surprising that 2 of the 77 tests yielded significant results.
Conclusion:
Therefore, it is not surprising that 2 of the 77 tests yielded significant results.
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Chapter 15 Solutions
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