Quiz 3_MATH302

Table of Contents

Part 1 of 3 –

Question 1 of 20 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: Round your answer to a whole number value as necessary. For example, 37 would be a legitimate entry.

Question 2 of 20 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.

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry.

Question 3 of 20 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?

Answer: Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry.

Question 4 of 20 1.0 Points

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?

Answer: Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry.

Question 5 of 20 1.0 Points

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.

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry.

Question 6 of 20 1.0 Points

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 . For example, .678 would be a legitimate entry. Place your UPPER limit, rounded to 3 decimal places, in the second blank . For example, .789 would be a legitimate entry.

Question 7 of 20 1.0 Points

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.

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry.

Part 2 of 3 –

Question 8 of 20 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

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Question 9 of 20 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

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Question 10 of 20 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

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Question 11 of 20 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

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Question 12 of 20 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

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Question 13 of 20 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

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Question 14 of 20 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

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Question 15 of 20 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

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Question 16 of 20 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)

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Question 17 of 20 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

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Question 18 of 20 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

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Part 3 of 3 –

Question 19 of 20 1.0 Points

In general, increasing the confidence level will narrow the confidence interval, and decreasing the confidence level widens the interval. True

False

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Question 20 of 20 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