# apu math302 quiz 3 done on may 2015

December 11, 2017

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.

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. 6.2

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

Key: 6.2|6.4, 9.2|9.3
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.

The personnel department of a large corporation wants to
estimate the family dental expenses of its employees to determine the
feasibility of providing a dental insurance plan. A random sample of 12
employees reveals the following family dental expenses (in dollars): 115, 370,
250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 99% confidence interval estimate for the
standard deviation of family dental expenses for all employees of this
corporation.

Place your LOWER limit, in dollars rounded to 1 decimal
place, in the first blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 98.4 would be a legitimate entry. 94.7

Place your UPPER limit, in dollars rounded to 1 decimal
place, in the second blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 567.8 would be a legitimate entry. 304.0

Question 3 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.

If a sample has 20 observations and a 95% confidence
estimate for f\$mu f\$ is needed, the
appropriate value of the t-multiple required is
2.093 . Place your answer, rounded to 3 decimal places, in the blank.
For example, 4.567 would be a legitimate entry.

Question 4 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.

A sample of 9 production managers with over 15 years of
experience has an average salary of \$71,000 and a sample standard deviation of
\$18,000.

Assuming that s = 18,000 is a reasonable estimate for
f\$sigma f\$ what sample size would be
needed to ensure that we could estimate the true mean salary of all production
managers with more than 15 years experience within \$4200 if we wish to be 95%
confident? Place your answer, as a whole number, in the blank. Do not use a
dollar sign, a comma, or any other stray mark. For examples, 34 would be a
legitimate entry. 71

Question 5 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?

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.

The personnel department of a large corporation wants to
estimate the family dental expenses of its employees to determine the
feasibility of providing a dental insurance plan. A random sample of 12
employees reveals the following family dental expenses (in dollars): 115, 370,
250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 95% confidence interval estimate for the standard
deviation of family dental expenses for all employees of this corporation.

Place your LOWER limit, in dollars rounded to 1 decimal
place, in the first blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 123.4 would be a legitimate entry. 104.7

Place your UPPER limit, in dollars rounded to 1 decimal
place, in the second blank. Do not use a dollar sign, a comma, or any other
stray mark. For example, 567.8 would be a legitimate entry. 251.1

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 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. 10.1

Part 2 of 3 – 8.0/
11.0 Points

Question 8 of 20
1.0/ 1.0 Points
In constructing a confidence interval estimate for a
population mean, when we replace f\$sigma f\$
with the sample standard deviation (s), we introduce a new source of
variability and the sampling distribution we use is:
A.the normal
distribution
B.chi-square
distribution
C.F- distribution
D.t -distribution

Question 9 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 < f\$sigma f\$ < 16.0 B.7.8 < f\$sigma f\$ < 13.8 C.74.0 < f\$sigma f\$ < 126.0 D.60.8 < f\$sigma f\$ < 190.5 Question 10 of 20 1.0/ 1.0 Points At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If the number of years of employment at this department store is normally distributed, what is the probability that a cashier selected at random has worked at the store for over 10 years? A.0.4916 B.0.9916 C.0.0084 D.0.0054 Question 11 of 20 1.0/ 1.0 Points A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked by employees in all payroll departments? A.301.0 < f\$mu f\$ < 319.6 B.298.0 < f\$mu f\$ < 322.6 C.302.2 < f\$mu f\$ < 318.4 D.314.1 < f\$mu f\$ < 316.8 Question 12 of 20 0.0/ 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) In C.(9.97, 10.80) D.(9.92, 10.08) Question 13 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 14 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 15 of 20 1.0/ 1.0 Points A researcher wishes to know, with 98% confidence, the percentage of women who wear shoes that are too small for their feet. A previous study conducted by the Academy of Orthopedic Surgeons found that 80% of women wear shoes that are too small for their feet. If the researcher wants her estimate to be within 3% of the true proportion, how large a sample is necessary? A.966 B.683 C.183 D.484 Question 16 of 20 0.0/ 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: In A.0.60 B.16.667 C..06 D.30 Question 17 of 20 1.0/ 1.0 Points If you are constructing a confidence interval for a single mean, the confidence interval will___________ with an increase in the sample size. A.decrease B.stay the same C.increase or decrease, depending on the sample data D.increase Question 18 of 20 0.0/ 1.0 Points In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university? A.1330 B.1400  C.1250 D.1100 Part 3 of 3 - 2.0/ 2.0 Points Question 19 of 20 1.0/ 1.0 Points The upper limit of the 95% confidence interval for the population proportion p, given that n = 300; and f\$hat{p}f\$ = 0.10 is approximately 0.1339. True False Question 20 of 20 1.0/ 1.0 Points The 95% confidence interval for the population mean f\$mu f\$ , given that the sample size n = 49 and the population standard deviation f\$sigma f\$ = 7, is f\$ar{X}pm 1.96f\$ . True False