11 Jun HOW LARGE A SAMPLE IS NEEDED IN ORDER TO B E 99 % CONFIDENT THAT THE SAMPLE PROPORTION WILL NOT DIFFER FROM THE TRUE PROPORTION BY MORE THAN 4%?
How large a sample is needed in order to b e 99 % confident that the sample proportion will not differ from the true proportion by more than 4%?
Statistics 1) In a recent survey, 70% of th e community favored building a health center in their neighborhood. If 1) 14 citizens are chosen, find the probability that exactly 6 of the m favor the building of th e health center. A) 0.023 B) 0.429 C) 0.700 D) 0.126 2) Fifty percent of th e people that use the Internet order something online. Find the probability that 2) only four of 8 Internet users will order something online. A) 0.004 B) 4.375 C) 0.273 D) 0.500 3) A quiz consists of 19 0 true or fals e questions. If the student guesses on each question, what is the 3) mean number of correct answers? A) 190 B) 38 C) 95 D) 0 Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid: 4) between $148,200 and $151,800 if the standard deviation is $1800 . 4) A) 34% B)99.7% C) 68% D) 95% Provide an appropriate response. 5) A physical fitness association is includin g the mile run in its secondary-school fitness test. The time 5) for this event for boys in secondary school is know n to possess a normal distribution with a mean of 460 seconds and a standard deviation of 6 0 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds. A) 0.4893 B) 0.9893 C) 0.0107 D) 0.5107 6) The length of tim e it takes college students to fin d a parking spot in the library parking lot follows 6) a normal distribution with a mean of 3.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 2.5 minutes. A) 0.3551 B) 0.1915 C) 0.2674 D) 0.3085 7) One year, professional sports players salaries averaged $1.6 million with a standard deviation of 7) $0.7 million. Suppose a sample of 10 0 major league players was taken. Find the approximate probability that the average salary of th e 100 players exceeded $1.1 million. A) 0.2357 B) approximately 1 C) 0.7357 D) approximatel y 0 8) Assume that the heights of me n are normally distributed with a mean of 67.9 inches and a standard 8) deviation of 2.1 inches. If 36 me n are randomly selected, find the probability that they have a mean height greater than 68.9 inches. A) 0.9979 B) 0.0210 C) 0.9005 D) 0.0021 1 9) Assume that blood pressure readings are normall y distributed with a mean of 12 2 and a standard 9) deviation of 9.6. If 14 4 people are randoml y selected, find the probability that their mean blood pressure will be less than 124. A) 0.9938 B) 0.9998 C) 0.0062 D) 0.8615 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 10) When 425 junior college students were surveyed, 190 said they have a passport. Construct 10) a 95% confidence interval for the proportio n of junio r college students that have a passport. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 11) Many people think that a national lobby’s successful fight against gun control legislation is 11) reflecting the wil l of a minority of Americans . A random sample of 400 0 citizens yielded 2250 who are in favo r of gu n control legislation. Estimate the tru e proportion of al l Americans who are i n favor of gu n control legislation using a 95% confidence interval. A) 0.4375 ± 0.4823 B) 0.4375 ± 0.0154 C) 0.5625 ± 0.0154 D) 0.5625 ± 0.4823 12) A researcher at a major clinic wishes to estimat e the proportio n of th e adult population of th e 12) United States that has sleep deprivation. How large a sample is neede d in orde r to b e 99 % confident that the sampl e proportion will not differ from the tru e proportion by mor e than 4%? A)2073 B) 1037 C) 17 D) 849 13) A senator wishes to estimate the proportion of Unite d States voters who favor abolishing the 13) Electoral College. How large a sample is neede d in orde r to b e 98 % confident that the sample proportion will not differ from the tru e proportion by mor e than 5%? A) 385 B) 54 3 C) 12 D) 1086 14) How much money does the averag e professional hockey fan spend on food at a single hockey 14) game? That question was pose d to 1 0 randoml y selected hockey fans. The sampled results show that sample mean and standard deviation were $19.00 and $3.35, respectively. Use this information t o create a 98% confidence interval for the mean. A) 19 ± 2.718(3.35/^10) B) 19 ± 2.262(3.35/-N/10) C) 19 ± 2.821(3.35/^/T0) D) 1 9 ± 2.764(3.35/^^) 15) Construct a 95 % confidence interval for the populatio n mean, fj. Assume the populatio n has a 15) normal distribution. A sample of 2 5 randomly English majors has a mean test score of 81. 5 with a standard deviation of 10.2. A) (87.12, 98.32) B) (77.29, 85.71) C) (66.35, 69.89) D) (56.12, 78.34) 2
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