The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,928 . Assume that the standard deviation is $2,903.

(a) What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $151 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

(b) What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.

A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within (plus/minus) $151 of m ranges from (blank) for a sample of size 30 to (blank) for a sample of size 400.

The Grocery Manufacturers of America reported that 65% of consumers read the ingredients listed on a product's label. Assume the population proportion is p=0.65 and a sample of 500 consumers is selected from the population.

(a) Show the sampling distribution of the sample proportion (p-bar) where, (p-bar) is the proportion of the sampled consumers who read the ingredients listed on a product's label. (1) E(p)= (xxxx) (2 decimals) (2) std dev of (p-bar) = (xxxx)

(b) What is the probability that the sample proportion will be within .03 of the population proportion (to 4 decimals).

(c) . Answer part (b) for a sample of 600 (to 4 decimals).

Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 18 seconds and 13 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.)

A =
（1 −7 5 0

0 10 8 2

2 4 10 3

−4 8 −9 6）

(1) Count the number of rows that contain negative components.
(2) Obtain the inverse of A and count the number of columns that contain even number of positive components.
(3) Assign column names (a,b,c,d) to the columns of A.
(4) Transform the matrix A into a vector object a by stacking rows.
(5) Replace the diagonal components of A with (0,0,2,3). Hint: use a “diag” function

Given that in 4 flips of a fair coin there are at least two "heads", what is the probability that there are two "tails"? There are ten equally likely outcomes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You randomly select one value, call it the initial value. Then, you continue to randomly select values, call them follow-up selections, until you come up with the initial value. What is the fewest number of follow-up selections that insures that the probability is better than one-half that you will observe your initial value? (Note: this problem assumes values are selected "with replacement," which simply means that after each selection, there are still the same ten equally likely outcomes.)

Say you’re an electrical engineer designing an electromechanical subassembly for use in a larger aircraft system. Twelve components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom, and the other end is the top. a. If all components are different, how many different design configurations are possible? b. If seven components are identical to one another, but the others are different, how many different design configurations are possible? c. If three components are of one type and identical to each other, and four components are of another type and identical to each other, but the others are different, how many different design configurations are possible?

1. One out of four Americans over age 55 has eaten pizza for breakfast. P(Eaten Pizza) = 0.25. If a sample of 10 Americans over the age of 55 is selected at random, find the probability that at most 3 have eaten pizza for breakfast. Use the binomial formula.

The manufacturer of a new line of ink-jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. The results from a sample of 14 cartridges can be found here

a. what is the point estimate of the population mean and standard deviation?

b. develop a 90% interval for the population mean

c. if the point estimate of the population mean and standard deviation are accurate, what is the probability that another sample of 14 cartridges will last an average of more than 1650 pages?

please show your work

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 443 grams with a standard deviation of 16. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

a. there is sufficient evidence that the bags are underfilled

b. there is not sufficient evidence that the bags are underfilled

There are 2 questions in this assignment.

1. Molly wants to pursue a graduate degree at New University but is unsure whether to specialize in law or medicine. To help her decide, she takes both the MCAT and LSAT exams.

LSAT: Molly's score = 120; Students at New University: M = 150, SD = 15

MCAT: Molly's score = 52; Students at New University: M = 40, SD = 6

Enter the data into SPSS and compute z-scores for each group of data.

Which graduate degree should Molly pursue?

In addition to your answer to the preceding question, copy and paste the SPSS output showing how you calculated this score and organize this in a Word document.

2. Amy and Sarah are arguing about who is smarter. They are the same major (psychology), they have identical GPAs (3.8), and attend the same university (Temple). They’ve decided that whoever had a higher college entrance exam is the more intelligent person. However, Amy took the ACT and Sarah took the SAT.

Amy earned a composite score of 24 on the ACT where there is a population mean of the ACT is 18 (σ = 6).

Sarah earned a composite score of 1,000 on the SAT where there is a population mean for the SAT is 906 (σ = 100).  

Compute the z-scores for Amy and Sarah using SPSS. According to their agreement, who is more intelligent?

In addition to your answer to the preceding question, copy and paste the SPSS output showing how you calculated this score and organize this in a Word document.

Our bodies produce heat from the work of keeping us alive. This heat is known as the body temperature, which is continuous and approximately normally distributed. The previous standard for a healthy body temperature was 98.6 F. However, the current average body temperature for a healthy human is 98.2 F, with a population standard deviation of 0.75 F

Single Subject

1. What is the probability of selecting a person who has a healthy body temperature (between 97 F and 100 F)?
2. What is the probability of selecting someone who has a body temperature of at least 100 F?
3. Find and interpret

4. Take your body temperature (in degrees Fahrenheit) and state it:

   1. Use your body temperature from above to find your percentile for body temperature.
   2. Interpret the percentile value you found above.

Groups of Subjects

Now, assume that you are creating a sampling distribution of by sampling a group of people.

5. State the expected mean and standard deviation for body temperatures in a group of 5 people.
6. What is the probability of selecting a group of 5 people with an average body temperature below 97 F?
7. What is the probability of selecting a group of 5 people who have a body temperature of at least 98 F?
8. What is the probability of selecting a group of 15 people who have a body temperature of at least 98 F?
9. Describe what happens to the standard deviation of the sampling distribution as group size increases. Include mathematical justification.

please show work, i dont understand how to do this what so ever. tysm

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 618 babies born in New York. The mean weight was 3404 grams with a standard deviation of 859 grams. Assume that birth weight data are approximately bell-shaped.

A. Estimate the number of newborns whose weight was less than 4263 grams.

Approximately ____ of the 618 newborns weighed less than 4263 gram

B. Estimate the number of newborns whose weight was greater than 1686 grams.

Approximately ____ of the 618 newborns weighed more than 1686 gram

C. Estimate the number of newborns whose weight was between 3404 and 5122 grams.

Approximately ____ of the 618 newborns weighed between 3404 and 5122 gram

Comparing Statistical Studies Statistics are all around us, whether or not we notice them being used. From public policy, health, economics, science, culture to which foods a fast-food restaurant is going to serve next can all be influenced by how the results of statistical studies are operationalized and interpreted. Each chapter of your course text concludes with two "Focus on" sections that go into depth on important issues of our time. The topics of these sections were chosen to demonstrate the great variety of fields in which statistics plays a role. For this Discussion, you are going to review and compare two statistical studies. To prepare for this Discussion: Think about your degree major and your areas of interests, and then concentrate on two of the following

Comparing Statistical Studies

Statistics are all around us, whether or not we notice them being used. From public policy, health, economics, science, culture to which foods a fast-food restaurant is going to serve next can all be influenced by how the results of statistical studies are operationalized and interpreted.

Each chapter of your course text concludes with two "Focus on" sections that go into depth on important issues of our time. The topics of these sections were chosen to demonstrate the great variety of fields in which statistics plays a role. For this Discussion, you are going to review and compare two statistical studies.

To prepare for this Discussion:

• Think about your degree major and your areas of interests, and then concentrate on two of the following "Focus on" disciplines: Agriculture, Criminology, Economics, Education, Environment, Health & Education, History, Law, Literature, Politics, Psychology, Public Health, Social Science, Sociology, or The Stock Market
• Review the readings from this week's Learning Resources, as well as the complete list of the "Focus on" topics to choose from
• Choose two of the studies to compare for this Discussion
• For each study, consider the sample population used, errors that could occur in the research process, and how meaningful and important the results of the study are

"Focus on" disciplines: Agriculture, Criminology, Economics, Education, Environment, Health & Education, History, Law, Literature, Politics, Psychology, Public Health, Social Science, Sociology, or The Stock Market Review the readings from this week's Learning Resources, as well as the complete list of the "Focus on" topics to choose from Choose two of the studies to compare for this Discussion For each study, consider the sample population used, errors that could occur in the research process, and how meaningful and important the results of the study are

An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed, what is the probability that the battery will perform reliably during a one-hour exam?

The Appalachian Bear Center (ABC) is a not-for-profit organization located near the Great Smoky Mountains National Park. ABC’s programs include the rehabilitation of orphaned and injured black bears, as well as research and education about Appalachian black bears. ABC provides the most natural environment possible for rehabilitating black bears before their release back into the wild. Katie Settlage performed a study to learn more about the Appalachian black bear population in the Great Smoky Mountains National Park. She and a team of researchers used a sample of 68 black bears in the park and took measurements such as paw size, weight, and shoulder height.

Answer the following questions based on this data. As always, you must show all work and formulas used in order to receive full credit. Round all decimals to three places unless otherwise noted.

1. In the sample of 68 bears, 40 were males. Construct an 80% confidence interval for the population proportion of bears that are males and write a statement interpreting the interval. (12 points)

Questions 2 and 3 refer to the following information regarding the 28 female bears from the study. For these 28 female bears, the sample mean is 75.679 cm and the sample standard deviation is 7.592 cm. Assume the data is normally distributed and the sample is randomly selected.

2. Use the female sample to make an interval estimate of the mean shoulder height of female bears. Construct the confidence interval estimate using a 95% confidence level and make a statement interpreting this interval.

3. Using a 99% level of confidence, construct the confidence interval for the population standard deviation based on the female data and make a statement interpreting these intervals.