# Mathematics

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 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.

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.

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##### Question 9 of 20
1.0 Points
Compute      where t15 has a t-distribution with 15 degrees of freedom.

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##### Question 10 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.

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##### Question 11 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?

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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?

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##### Question 13 of 20
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?

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##### Question 14 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

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##### Question 15 of 20
1.0 Points
Confidence intervals are a function of which of the following three things?

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##### Question 16 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.

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##### Question 17 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?

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##### Question 18 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:

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 Part 3 of 3 –
##### Question 19 of 20
1.0 Points
A 90% confidence interval estimate for a population mean is determined to be 72.8 to 79.6. If the confidence level is reduced to 80%, the confidence interval becomes narrower.

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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.

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