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# Exercises

1. Given the following results obtained from random samples from infinite binomial populations, find the best estimate for p and the standard error of :
a. n = 25, X = 10
b. n = 64, X = 32
c. n = 100, X = 64
d. n = 400, X = 140
2. Out of a sample of 1000 individuals, 672 gave the answer “yes” to a particular question. What is the best estimate of p, the proportion of those who would respond “yes?” What is the standard error of ?
3. Assuming a large population, describe the sampling distribution of for each of the following cases:
a. n = 300, p = 0.07
b. n = 500, p = 0.04
c. n = 1000, p = 0.10
d. n = 100, p = 0.75
4. Suppose a random sample of size n = 75 is extracted from an infinite (binomial) population and the proportion of items in the population with a given property is p = 0.8. Describe the sampling distribution of . Also, find:
a. The probability of obtaining at least X = 65 items with the property.
b. The probability of obtaining fewer than X = 25 items with ...

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