30 The middle interval around the population proportion which captures 95% of sa

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30 The middle interval around the population proportion which captures 95% of sample proportions of vehicles that exceed the speed limit is: (0.726, 0.794) What was the sample size used to build this interval? a 665 b 650 c 632 d 607 Question 31-33 are related 31 Among adult residents of a certain state 81% have 12 or more years of schooling. In repeated samples of 600 residents what is the standard error of the sample proportion? a 0.0139 b 0.0148 c 0.0160 d 0.0175 32 In repeated samples of 600 residents what fraction of sample proportions are within ±0.04 (4 percentage points) of the population proportion? a 0.9876 b 0.9452 c 0.9356 d 0.9282 33 In the previous question, if you doubled the sample size, what is the middle interval around the population proportion that would capture 98% of sample proportions? a 0.801 0.819 b 0.796 0.824 c 0.790 0.830 d 0.784 0.836 34 Rick O'Shea is one of the two candidates running for the governor of a Midwestern state. Suppose Rick O'Shea has 48 percent of the votes among all the voters in the state. Just before the election a local TV news polls a random sample of 400 voters. What is the probability that the poll will predict Rick O'Shea winning the election? a 0.1151 b 0.1762 c 0.1922 d 0.2119 35 What should the sample size be in order to reduce the probability of wrongly predicting Rick O'Shea's victory to 0.025? a 2824 b 2398 c 2196 d 1925 30 The middle interval around the population proportion which captures 95% of sample proportions of vehicles that exceed the speed limit is: (0.726, 0.794) What was the sample size used to build this interval? a 665 b 650 c 632 d 607 Question 31-33 are related 31 Among adult residents of a certain state 81% have 12 or more years of schooling. In repeated samples of 600 residents what is the standard error of the sample proportion? a 0.0139 b 0.0148 c 0.0160 d 0.0175 32 In repeated samples of 600 residents what fraction of sample proportions are within ±0.04 (4 percentage points) of the population proportion? a 0.9876 b 0.9452 c 0.9356 d 0.9282 33 In the previous question, if you doubled the sample size, what is the middle interval around the population proportion that would capture 98% of sample proportions? a 0.801 0.819 b 0.796 0.824 c 0.790 0.830 d 0.784 0.836 34 Rick O'Shea is one of the two candidates running for the governor of a Midwestern state. Suppose Rick O'Shea has 48 percent of the votes among all the voters in the state. Just before the election a local TV news polls a random sample of 400 voters. What is the probability that the poll will predict Rick O'Shea winning the election? a 0.1151 b 0.1762 c 0.1922 d 0.2119 35 What should the sample size be in order to reduce the probability of wrongly predicting Rick O'Shea's victory to 0.025? a 2824 b 2398 c 2196 d 1925

Explanation / Answer

for 30 data required

31) standard error of the sample proportion =(p*(1-p)/n)1/2 =0.0160

option C

32)

option A

33)

for n=1200 ;std error =0.0113

and for middle 98% ; critical z =2.326

hence 98% CI = p-/+ z*std error =0.784 ; 0.836

optin D

34)

option D

35)

for 0.025 highest value z =1.96

therefore required sample size =((0.50-0.48)/(z*(p*(1-p))1/2)2 =2398

probability = P(0.77<X<0.85) = P(-2.4976<Z<2.4976)= 0.9937-0.0063= 0.9876

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