Consider a large-sample level 0.01 test for testing
H0: p = 0.2
against Ha: p > 0.2.
(a) For the alternative value p = 0.21, compute β(0.21) for sample sizes n = 100, 1600, 10,000, 40,000, and 90,000. (Round your answers to four decimal places.)
n | β |
---|---|
100 | |
1600 | |
10,000 | |
40,000 | |
90,000 |
(b) For p̂ = x/n = 0.21, compute the
P-value when n = 100, 1600, 10,000, and 40,000.
(Round your answers to four decimal places.)
n | P-value |
---|---|
100 | |
1600 | |
10,000 | |
40,000 |
(c) In most situations, would it be reasonable to use a level 0.01
test in conjunction with a sample size of 40,000? Why or why
not?
Yes, even when the departure from H0 is significant from a practical point of view, a statistically significant result is not likely to appear; it is difficult for the test to detect departures from H0.Yes, it is always advantageous to have a very large sample size, because it will detect very small departures from H0. No, even when the departure from H0 is insignificant from a practical point of view, a statistically significant result is highly likely to appear; the test is too likely to detect small departures from H0.No, it is never advantageous to have a very large sample size, because it cannot detect very small departures from H0.
You may need to use the appropriate table in the Appendix of Tables
to answer this question.
a)
n | beta |
100 | 0.9793 |
1600 | 0.9032 |
10000 | 0.4325 |
40000 | 0.0040 |
90000 | 0.0000 |
b)
n | p value |
100.0000 | 0.4013 |
1600.0000 | 0.1587 |
10000.0000 | 0.0062 |
40000.0000 | 0.0000 |
c)
No, even when the departure from H0 is insignificant from a practical point of view, a statistically significant result is highly likely to appear; the test is too likely to detect small departures from H0.
Consider a large-sample level 0.01 test for testing H0: p = 0.2 against Ha: p >...
Consider a large-sample level 0.01 test for testing H0: p = 0.2 against Ha: p > 0.2. (a) For the alternative value p = 0.21, compute β(0.21) for sample sizes n = 100, 1600, 12,100, 40,000, and 90,000. (Round your answers to four decimal places.) n β 100 _____ 1600 _____ 12100 _____ 40000 _____ 90000 _____ (b) For p̂ = x/n = 0.21, compute the P-value when n = 100, 1600, 12,100, and 40,000. (Round your answers to four...
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