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Quiz 3 | Complete Solution
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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.

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

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 4 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.

A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval estimate for the average number of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal place, in the blanks. Place you lower limit in the first blank.   Place your upper limit in the second blank.   When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 12.3 would be a legitimate entry.
Question 5 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 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.

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.

Question 6 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 percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives.

Determine a 95% confidence interval for the proportion defective for the process today.

Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer.

Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.

Question 7 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.

A sample of 40 country CD recordings of Willie Nelson has been examined. The average playing time of these recordings is 51.3 minutes, and the standard deviation is s = 5.8 minutes.

Using an appropriate t-multiplier, construct a 95% confidence interval for the mean playing time of all Willie Nelson recordings.

Place your LOWER limit, in minutes, rounded to 2 decimal places, in the first blank. For example, 56.78 would be a legitimate entry.  .

Place your UPPER limit, in minutes, rounded to 2 decimal places, in the second blank. For example, 67.89 would be a legitimate entry.

Part 2 of 3 -

Question 8 of 20    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

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Question 9 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 10 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 11 of 20    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

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Question 12 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 13 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..06

C.0.60

D.16.667

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Question 14 of 20    1.0 Points
Confidence intervals are a function of which of the following three things?

A.The data in the sample, the confidence level, and the sample size

B.The population, the sample, and the standard deviation

C.The sampling distribution, the confidence level, and the degrees of freedom
D.The sample, the variable of interest, and the degrees of freedom

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Question 15 of 20    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.increase

B.increase or decrease, depending on the sample data
C.stay the same

D.decrease

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Question 16 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.0.5316

B.0.7342

C.0.2658

D.0.4684

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Question 17 of 20    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

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Question 18 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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Part 3 of 3 -

Question 19 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 0.2341.

True

False

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Question 20 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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Quiz 3 | Complete Solution
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