ssignment Thity-three percent of all Americans drink bottled water more than onc

Question

ssignment Thity-three percent of all Americans drink bottled water more than once a week (Natural resources Defense Councal, December 4, 2015]. Suppose you have been hired by the Natural Resources Defence Council to invetigate bottled water consumption in St. Paud., You plan to select a sample of St. Paulites to estimate the proportion who drink bottled water more than ance a week. Assume the sample proportion of St. Paulites to estimate the proportion who drink bottled water more than once a week is 0.33, the same as the overall proportion af americans who drink bettled water more than once a week. Use z-table. a. Suppose you select a sample of 540 St.Paultes. Show the sampling distribution of?(to 4 decimals). 0.0202 b. Based upon a sample of 540 st. Paulites, what is the probability that the sample proportion will be within 0.04 of the population proportion (to 4 decimals). probabiity c Suppose you select a sample of 170 St.Paulites, Show the sampling dstribution of jF (to 4 decdimals). )0.33 ?- 0.0361 : ? d. Based upon a smaller sample of only 170 St. Paultes, what is the probability that the sample proportion wl be within 0.04 of the population proportion (to 4 decimals) probability -0.0361 e. As measured by the increase in probability, how much do you pain in precision by taking the larger sample in parts (a) and (b) rather than the smaller sample in parts (c) and (d)? 0.731 dax Type here to search

Explanation / Answer

Answering only the wrong questions

b. So thesample proportion p should be between 0.33-0.04 and 0.33+0.04

P(0.29<Pˆ<0.37)=P((0.29??P)/?P<Z<(0.37??P)/?P)

=P((0.29?0.33)/0.0202<Z<(0.37-0.33/0.0202))

=P(?1.9802<Z<1.98018)

=P(1.98018)?P(?1.9802)

= 0.9523

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Answering only the wrong questions

d. So thesample proportion p should be between 0.33-0.04 and 0.33+0.04

Calculating ?P

?P = sqrt(pq/n)=sqrt(0.33(1-0.33)/170) =

0.036064

P(0.29<Pˆ<0.37)=P((0.29??P)/?P<Z<(0.37??P)/?P)

=P((0.29?0.33)/0.036064<Z<(0.37-0.33/0.036064))

=P(?1.10914<Z<1.10914)

=P(1.10914)?P(?1.10914)

=

0.7326

e. Reduced by21%[0.21969]

=0.976159358852324000 - 0.023840641147675700

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