Question: If a sample constitutes an appreciable portion of a population
If a sample constitutes an appreciable portion of a population, that is, more than 5 percent of the population according to the rule of thumb given on page 239, the formulas of Theorems 11.1 and 11.2 must be modified by using the variance formula of Theorem 8.6 on page 238 instead of that of Theorem 8.1 on page 233. For instance, the maximum error in Theorem 11.1 becomes
Use this modification to rework Exercise 11.20, given that there are 900 sixth graders in the school district.
Answer to relevant QuestionsUse the modification suggested in Exercise 11.26 to rework Exercise 11.21, given that there are 900 sixth graders in the school district. A major truck stop has kept extensive records on various transactions with its customers. If a random sample of 18 of these records shows average sales of 63.84 gallons of diesel fuel with a standard deviation of 2.75 ...Show that the (1 – α) 100% confidence interval Is shorter than the (1 – α) 100% confidence interval Among 500 marriage license applications chosen at random in a given year, there were 48 in which the woman was at least one year older than the man, and among 400 marriage license applications chosen at random six years ...Show that if x is used as a point estimate of µ and s is known, the probability is 1 – α that | – µ|, the absolute value of our error, will not exceed a specified amount e when (If it turns out that n < 30, this ...
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