Example 5.4 can be solved with the bitesti command. We supply the value of n k and p. We see the probability that X <= 1 is .7361, as shown in the book.
bitesti 10 1 .1
N Observed k Expected k Assumed p Observed p
------------------------------------------------------------
10 1 1 0.10000 0.10000
Pr(k >= 1) = 0.651322 (one-sided test)
Pr(k <= 1) = 0.736099 (one-sided test)
Pr(k <= 1 or k >= 2) = 1.000000 (two-sided test)
Example 5.5 also can be solved with bitesti. In this example, the N is 12, k is 5, and p is .25. Stata shows that the probability of missing 5 or more shots is .1576.
bitesti 12 5 .25
N Observed k Expected k Assumed p Observed p
------------------------------------------------------------
12 5 3 0.25000 0.41667
Pr(k >= 5) = 0.157644 (one-sided test)
Pr(k <= 5) = 0.945598 (one-sided test)
Pr(k <= 0 or k >= 5) = 0.189320 (two-sided test)
We can also solve example 5.7 using bitesti, as shown below. Stata shows the probablity X >= 1450 is .9802, as shown in the book.
bitesti 2500 1450 .6
N Observed k Expected k Assumed p Observed p
------------------------------------------------------------
2500 1450 1500 0.60000 0.58000
Pr(k >= 1450) = 0.980180 (one-sided test)
Pr(k <= 1450) = 0.021854 (one-sided test)
Pr(k <= 1450 or k >= 1550) = 0.043274 (two-sided test)
We can solve example 5.10 using bitesti as shown below.
bitesti 100 9 .1
N Observed k Expected k Assumed p Observed p
------------------------------------------------------------
100 9 10 0.10000 0.09000
Pr(k >= 9) = 0.679126 (one-sided test)
Pr(k <= 9) = 0.451290 (one-sided test)
Pr(k <= 9 or k >= 11) = 0.868135 (two-sided test)
We skip examples 5.11 and 5.12.
Show example 5.21 on page 416.
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