Ask Statistics and Probability Expert

1. Using http://onlinestatbook.com/stat_sim/sampling_dist/index.html, select a population distribution that isNOT normal (i.e., heavily skewed, uniform, bimodal). Using the same population distribution for each, construct the distribution of sample means for and .  Take at least 10,000 samples.

a. Include a screen shot of your parent population and your two distributions of sample means here.

b. How are your two distributions of sample means similar? How are they different?

c. Describe how your results relate to the Central Limit Theorem.

2. For the following questions, assume a normally distributed population.

a. Given μ, σ, and , compute the standard error of the mean.

b. Given μ, σ, and , compute the standard error of the mean.

c. Given μ, σ, and , compute the standard error of the mean.

d. Given μ, σ, and , compute the standard error of the mean.

e. How does the standard error of the mean change when the population mean, population standard deviation, and sample size change?

3. Vehicle speeds at a certain highway location are normally distributed with a mean of 70 mph and standard deviation of 10 mph. For each of the following questions, fill in the blank with the appropriate speeds. You may apply the Empirical Rule where appropriate.

Hint: Pay careful attention to whether you are dealing with a distribution of individual observations or a distribution of sample means. The standard deviation that you use will differ for each (i.e., standard deviation versus standard error of the mean).

a. One vehicle is randomly selected; there is about a 68% chance that the vehicle's speed will be between ___and ___.

b. One vehicle is randomly selected; there is about a 99.7% chance that the vehicle's speed will be between ___and ___.

c. The speeds of randomly selected samples of 25 vehicles will be recorded. For samples of vehicles, there is about a 68% chance that a sample's mean speed will be between ___ and ___.

d. The speeds of randomly selected samples of 25 vehicles will be recorded. For samples of vehicles, there is about a 99.7% chance that a sample's mean speed will be between ___ and ___.

4. ACT scores have a mean (μ) of 18 and a standard deviation (σ) of 6. Suppose that we are taking a simple random sample of 40 students from one high school.

a. Calculate the standard error of the mean.

b. If we were to repeatedly pull samples of 40 individuals from the population of all ACT test takers, the distribution of sample means would have a mean of ____ and a standard deviation of ____.

c. Given the values from part (b), 95% of samples of will have sample means between ___ and ___.

d.  What is the probability that you would pull a random sample of 40 individuals from the population of all test takers and they would have a sample mean of 20 or higher?

e. Suppose that the high school in question boasts that their students (i.e., the population of all of their students) have an average ACT score above the national average of 18. In your sample of 40 students from that school, you compute a sample mean of 20. Is it likely that the mean in the population of all students at this school is less than 18? In other words, do you think these sample results (x-bar = 20) could be due to sampling error? Or, do you think there is evidence to state that the mean ACT score of students at this high school is above 18? Explain your reasoning.     Hint: Refer back to your answer from part (d).

5. World Campus wants to estimate the proportion of its students who are over the age of 40. In a sample of 100 World Campus students, 21 students were over the age of 40.

a. Compute the sample proportion (p-hat).

b. Compute the standard error of the sample proportion. Use the sample proportion as an estimate of the population proportion because at this point we do not have a population parameter.

c. Verify that it is appropriate to use normal approximation methods with the data from this study.

d. An article online claims that 17% of all World Campus students are over the age of 40.  What is the probability that a population where p=.17 would produce a random sample of with a sample proportion as high (or higher) than the one that you computed in part a?

In other words, given that the population proportion (p) is .17, what proportion of samples of would have a sample proportion greater than the one that you observed in your sample?

You will need to compute the standard error again because now we have a population parameter: p=.17

e. Given your results from part (d), do you think that the article's claim that the population proportion is .17 could be accurate? Or, do you think that their claim is an underestimate of the true proportion of World Campus students who are over the age of 40? Explain your reasoning.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M91923131
  • Price:- $30

Priced at Now at $30, Verified Solution

Have any Question?


Related Questions in Statistics and Probability

Introduction to epidemiology assignment -assignment should

Introduction to Epidemiology Assignment - Assignment should be typed, with adequate space left between questions. Read the following paper, and answer the questions below: Sundquist K., Qvist J. Johansson SE., Sundquist ...

Question 1 many high school students take the ap tests in

Question 1. Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year,of the 211,693 students who too ...

Basic statisticsactivity 1define the following terms1

BASIC STATISTICS Activity 1 Define the following terms: 1. Statistics 2. Descriptive Statistics 3. Inferential Statistics 4. Population 5. Sample 6. Quantitative Data 7. Discrete Variable 8. Continuous Variable 9. Qualit ...

Question 1below you are given the examination scores of 20

Question 1 Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file). 52 99 92 86 84 63 72 76 95 88 92 58 65 79 80 90 75 74 56 99 a. Construct a frequency distributi ...

Question 1 assume you have noted the following prices for

Question: 1. Assume you have noted the following prices for paperback books and the number of pages that each book contains. Develop a least-squares estimated regression line. i. Compute the coefficient of determination ...

Question 1 a sample of 81 account balances of a credit

Question 1: A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126. 1. Formulate the hypotheses that can be used to determine whether the mean of all acc ...

5 of females smoke cigarettes what is the probability that

5% of females smoke cigarettes. What is the probability that the proportion of smokers in a sample of 865 females would be greater than 3%

Armstrong faber produces a standard number-two pencil

Armstrong Faber produces a standard number-two pencil called Ultra-Lite. The demand for Ultra-Lite has been fairly stable over the past ten years. On average, Armstrong Faber has sold 457,000 pencils each year. Furthermo ...

Sppose a and b are collectively exhaustive in addition pa

Suppose A and B are collectively exhaustive. In addition, P(A) = 0.2 and P(B) = 0.8. Suppose C and D are both mutually exclusive and collectively exhaustive. Further, P(C|A) = 0.7 and P(D|B) = 0.5. What are P(C) and P(D) ...

The time to complete 1 construction project for company a

The time to complete 1 construction project for company A is exponentially distributed with a mean of 1 year. Therefore: (a) What is the probability that a project will be finished in one and half years? (b) What is the ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As