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##### MATH302 QUIZ 3

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Question;Question 1 of 20 1.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For scientific;notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;Assume 50 random samples of the same sample size are taken;from a population, and a 90% confidence interval is constructed from each;sample. How many of the intervals would you expect to contain the true;population mean?;Answer: 45 Round your;answer to a whole number value as necessary.;For example, 37 would be a legitimate entry.;Question 2 of 20 1.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;Senior management of a consulting services firm is concerned;about a growing decline in the firm?s weekly number of billable hours. The firm;expects each professional employee to spend at least 40 hours per week on work.;In an effort to understand this problem better, management would like to;estimate the standard deviation of the number of hours their employees spend on;work-related activities in a typical week. Rather than reviewing the records of;all the firm?s full-time employees, the management randomly selected a sample;of size 51 from the available frame. The sample mean and sample standard;deviations were 48.5 and 7.5 hours, respectively.;Construct a 99% confidence interval for the standard;deviation of the number of hours this firm?s employees spend on work-related;activities in a typical week.;Place your LOWER limit, in hours, rounded to 1 decimal;place, in the first blank. For example, 6.7 would be a legitimate entry. 5.9;Place your UPPER limit, in hours, rounded to 1 decimal;place, in the second blank. For example, 12.3 would be a legitimate entry. 10;Question 3 of 20 0.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;The manufacturer of a new compact car claims the miles per;gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a;mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are;tested, what is the probability the average mpg achieved by these 30 cars will;be greater than 28?;Feedback: This is a sampling distribution problem with? =;25.9.? = 9.5, and sample size n = 30.;P(z > 1.210755) = 1 ? NORMSDIST(1.210755) = 0.1130;Or you can compute the probability without having to compute;z first;P(x-bar > 28) = 1 ? NORMDIST(28, 25.9, 9.5/SQRT(30);TRUE) = 0.1130;Question 4 of 20 0.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;The manufacturer of a new compact car claims the miles per;gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a;mean of 24.6 mpg and a standard deviation of 11.2 mpg. If 30 such cars are tested, what is the;probability the average mpg achieved by these 30 cars will be greater than 27?;Feedback: This is a sampling distribution problem with? =;24.6.? = 11.2, and sample size n = 30.;P(z > 1.173691) = 1 - NORMSDIST(1.173691) = 0.1203;Or you can compute the probability without having to compute;z first;P(x-bar > 27) = 1 - NORMDIST(27, 24.6, 11.2/SQRT(30);TRUE) = 0.1203;Question 5 of 20 1.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;Senior management of a consulting services firm is concerned;about a growing decline in the firm?s weekly number of billable hours. The firm;expects each professional employee to spend at least 40 hours per week on work.;In an effort to understand this problem better, management would like to;estimate the standard deviation of the number of hours their employees spend on;work-related activities in a typical week. Rather than reviewing the records of;all the firm?s full-time employees, the management randomly selected a sample;of size 51 from the available frame. The sample mean and sample standard;deviations were 48.5 and 7.5 hours, respectively.;Construct a 95% confidence interval for the standard;deviation of the number of hours this firm?s employees spend on work-related;activities in a typical week.;Place your LOWER limit, in hours, rounded to 1 decimal;place, in the first blank. For example, 6.7 would be a legitimate entry. 6.3;Place your UPPER limit, in hours, rounded to 1 decimal;place, in the second blank. For example, 12.3 would be a legitimate entry. 9.3;Question 6 of 20 1.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;You are told that a random sample of 150 people from Iowa;has been given cholesterol tests, and 60 of these people had levels over the;?safe? count of 200. Construct a 95% confidence interval for the population;proportion of people in Iowa with cholesterol levels over 200. Place your LOWER;limit, rounded to 3 decimal places, in the first blank.321.;For example,.678 would be a legitimate entry. Place your UPPER limit, rounded to 3 decimal;places, in the second blank.483. For;example,.789 would be a legitimate entry.;Question 7 of 20 1.0/;1.0 Points;Accepted characters: numbers, decimal point markers (period;or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000);E" or "e" (used in scientific notation). NOTE: For;scientific notation, a period MUST be used as the decimal point marker.;Complex numbers should be in the form (a + bi) where;a" and "b" need to have explicitly stated values.;For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is;valid whereas {9i} is not.;Senior management of a consulting services firm is concerned;about a growing decline in the firm?s weekly number of billable hours. The firm;expects each professional employee to spend at least 40 hours per week on work.;In an effort to understand this problem better, management would like to;estimate the standard deviation of the number of hours their employees spend on;work-related activities in a typical week. Rather than reviewing the records of;all the firm?s full-time employees, the management randomly selected a sample;of size 51 from the available frame. The sample mean and sample standard;deviations were 48.5 and 7.5 hours, respectively.;Construct a 90% confidence interval for the standard;deviation of the number of hours this firm?s employees spend on work-related;activities in a typical week.;Place your LOWER limit, in hours, rounded to 1 decimal;place, in the first blank. For example, 6.7 would be a legitimate entry. 6.5;Place your UPPER limit, in hours, rounded to 1 decimal;place, in the second blank. For example, 12.3 would be a legitimate entry. 9.0;Part 2 of 3 - 9.0/;11.0 Points;Question 8 of 20 1.0/;1.0 Points;The average gas mileage of a certain model car is 26 miles;per gallon. If the gas mileages are normally distributed with a standard;deviation of 1.3, find the probability that a randomly selected car of this;model has a gas mileage between 25.8 and 26.3 miles per gallon.;A.0.15;B.0.85;C.0.70;D.0.30;Question 9 of 20 1.0/;1.0 Points;A recent study of 750 Internet users in Europe found that;35% of Internet users were women. What is the 95% confidence interval estimate;for the true proportion of women in Europe who use the Internet?;A.0.321 < p < 0.379;B.0.316 < p < 0.384;C.0.309 < p < 0.391;D.0.305 < p < 0.395;Question 10 of 20 0.0/;1.0 Points;When you calculate the sample size for a proportion, you use;an estimate for the population proportion, namely. A conservative value for n can be obtained;by using = ______.;A.0.05;B.0.10;C.0.01;D.0.50;Question 11 of 20 1.0/;1.0 Points;From a sample of 500 items, 30 were found to be defective.;The point estimate of the population proportion defective will be;A.30;B.16.667;C..06;D.0.60;Question 12 of 20 1.0/;1.0 Points;Find the 95% confidence interval for the standard deviation;of the lengths of pipes if a sample of 26 pipes has a standard deviation of 10;inches.;A.14.0;< 16.0;B.7.8;< 13.8;C.74.0;< 126.0;D.60.8;< 190.5;Question 13 of 20 1.0/;1.0 Points;The upper limit of the 90% confidence interval for the;population proportion p, given that n = 100, and = 0.20 is;A.0.4684;B.0.5316;C.0.7342;D.0.2658;Question 14 of 20 1.0/;1.0 Points;A previous study of nickels showed that the standard;deviation of the weight of nickels is 150 milligrams. How many nickels does a;coin counter manufacturer need to weigh so that she can be 98% confident that;her sample mean is within 25 milligrams of the true average weight of a nickel?;A.36;B.196;C.239;D.139;Question 15 of 20 1.0/;1.0 Points;In a study of elephants a researcher wishes to determine the;average weight of a certain subspecies of elephants. From previous studies, the;standard deviation of the weights of elephants in this subspecies is known to;be 1500 pounds. How many elephants does the researcher need to weigh so that he;can be 80% confident that the average weight of elephants in his sample is;within 350 pounds of the true average weight for this subspecies?;A.39;B.166;C.50;D.31;Question 16 of 20 1.0/;1.0 Points;A food snack manufacturer samples 15 bags of pretzels off;the assembly line and weighed their contents. If the sample mean is 10.0 and;the sample standard deviation is 0.15, find the 95% confidence interval;estimate for the true mean.;A.(9.96, 10.04);B.(9.68, 10.32);C.(9.97, 10.80);D.(9.92, 10.08);Question 17 of 20 0.0/;1.0 Points;Which of the following will make a confidence interval;narrower and more precise?;A.Larger sample size and lower confidence;level;B.Larger sample size and higher confidence;level;C.Smaller sample size and higher confidence;level;D.Smaller sample size and lower confidence;level;Question 18 of 20 1.0/;1.0 Points;Compute where t20;has a t-distribution with 20 degrees of freedom.;A.0.1767;B.0.5334;C.0.8233;D.0.6466;Part 3 of 3 - 0.0/;2.0 Points;Question 19 of 20 0.0/;1.0 Points;In general, increasing the confidence level will narrow the;confidence interval, and decreasing the confidence level widens the interval.;True;False;Question 20 of 20 0.0/;1.0 Points;The lower limit of the 95% confidence interval for the;population proportion p, given that n = 300, and = 0.10 is 0.1339.;True;False

Paper#60599 | Written in 18-Jul-2015

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