# Project #3868 - Statistics (20 Questions)

Question 1 of 20 1.0 Points

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 2 of 20 1.0 Points

If a sample has 25 observations and a 99% 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, 3.456 would be an appropriate entry.
Question 3 of 20 1.0 Points

You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been    \$1200. If you want to be 99% sure that you have estimated average family food expenditures within \$60, how many families do you need to survey?  Place your answer, a whole number, in the blank  . For example, 1234 would be a legitimate entry.
Question 4 of 20 1.0 Points

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 5 of 20 1.0 Points

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 the salaries of production managers with over 15 years experience are normally distributed, you can be 95% confident that the mean salary for all production managers with at least 15 years of experience is between what two numbers.

Place your LOWER limit, rounded to a whole number, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 54321 would be a legitimate entry.  . Place your UPPER limit, rounded to a whole number, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 65432 would be a legitimate entry.

Question 6 of 20 1.0 Points

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

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
The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.

A. n - 2

B. n - 1

C. n + 1

D. n

Question 9 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. 166

B. 50

C. 39

D. 31

Question 10 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

Question 11 of 20 1.0 Points
In constructing a confidence interval estimate for a population mean, when we replace   with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution we use is:

A. chi-square distribution

B. F- distribution

C. t -distribution

D. the normal distribution

Question 12 of 20 1.0 Points
Confidence intervals are a function of which of the following three things?

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

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

C. The sampling distribution, the confidence level, and the degrees of freedom

D. The sample, the variable of interest, and the degrees of freedom

Question 13 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

Question 14 of 20 1.0 Points
If you increase the confidence level, the confidence interval ____________.

A. may increase or decrease, depending on the sample data

B. stays the same

C. decreases

D. increases

Question 15 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. .06

B. 30

C. 16.667

D. 0.60

Question 16 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

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?

A. 1330

B. 1400

C. 1250

D. 1100

Question 18 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. 0.01

B. 0.05

C. 0.50

D. 0.10

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.

True

False

Question 20 of 20 1.0 Points
In developing a confidence interval for the population standard deviation,   , we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution, but rather a right-skewed distribution called the chi-square distribution, which (for this procedure) has n – 1 degrees of freedom.

True

False

 Subject Mathematics Due By (Pacific Time) 04/04/2013 07:00 pm
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