Suppose a polling organization takes a random sample of 100 people from the popu

Question

Suppose a polling organization takes a random sample of 100 people from the population of adults in a city, (where 30% of this population wants to get rid of the penny). Then the probability is 0.015 that the sample proportion who want to get rid of the penny is less than 0.20.  Stating, "If you repeatedly select a sample of 100 adults from this city and record the proportion that want to get rid of the penny for each sample, in the long run roughly 1.5% of these samples will have at most 20% of the sample wanting to get rid of the penny," would explain what it means to say "the probability of …" while describing the random process that is repeated over and over again.

TRUE OR FALSE ?

Explanation / Answer

Sample size = 100

so proportion of the people who want to get rid of the penny is less than 0.20 = 0.015

Here p0 or say population proportion = 0.30

so standard error of the proportion = sqrt [ p * (1-p) //N] = sqrt p 0.3 * 0.7/100] = 0.0458

=> Pr ( p < 0.20 ; 0.3 ; 0.0458) = ?

Z = (0.20 - 0.30)/ 0.0458 = -2.183

so value of P from Z - table is Pr ( p < 0.20 ; 0.3 ; 0.0458) = 0.015

so it is true that "If you repeatedly select a sample of 100 adults from this city and record the proportion that want to get rid of the penny for each sample, in the long run roughly 1.5% of these samples will have at most 20% of the sample wanting to get rid of the penny' SO, the given statement is true.

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