MATH 2311-Television viewers often express doubts about the validity of certain commercials

Subject: Mathematics / Statistics
Question
Question 12

Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 97% confident that their estimate will fall within 1% of the true population proportion?

a) 11302

b) 11313

c) 11316

d) 11296

e) 11285

f) None of the above

Question 13

An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 3% of the true proportion with 95% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?

a) 1079

b) 1060

c) 1053

d) 1074

e) 1068

f) None of the above

Question 14

It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 116 people in the first group and this group will be administered the new drug. There are 210 people in the second group and this group wil be administered a placebo. After one year, 11% of the first group has a second episode and 18% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.

a) [-0.635, 0.495]

b) [-0.135, -0.005]

c) [-0.147, 0.007]

d) [-0.007, 0.147]

e) [0.005, 0.012]

f) None of the above

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