Statistics Questions

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12) Why do we have a margin of error in statistics? If statistics are meant to be accurate, why are they sometimes accompanied by an estimate of doubt?

Discuss the concept of Margin of error as it relates to sample size.

Find at least examples of 3 studies or reports online that used a margin of error to draw conclusions or make a prediction. Respond to at least two other post

11)

After completing Assignment 4 (Module 6) located in Confidence Interval for Means Page on Canvas, discuss:

( a) The differences between the Z- interval and T- interval.

(b) What determines when to use Z interval and T interval

(c ) Which interval would be appropriate to use for the project? Justify your answer.

Module 7 )

1. An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 19 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.24,respectively. Is there enough evidence to reject the company’s claim at ? = 0.05? Assume the population is normally distributed .

2. Susan goes to her doctor because she thinks she is ill.
(a) What is H0, Ha?

(b) Type I error? Type II error?

(c) Which of the errors are more serious and why?

Module 6 )

Q 1.

According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source:Data from The Boston Globe October 17, 2006.)

a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes.

b. In a course you are taking with 100 students, half of the students have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 students who have blue eyes.

c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.

Q 2.

An exam consists of 50 multiple-choice questions. Based on how much you studied, for any given question you think you have a probability of p=0.70 of getting the correct answer. Consider the sampling distribution of the sample proportion of the 50 questions on which you get the correct answer.

a. Find the mean and standard deviation of the sampling distribution of this proportion.

b.What do you expect for the shape of the sampling distribution? Why?

c. If truly p=0.70, would it be very surprising if you got correct answers on only 60% of the questions? Justify your answer by using the normal distribution to approximate the probability of a sample proportion of 0.60 or less.

Statistics questions

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I’m trying to learn for my Statistics class and I’m stuck. Can you help?

EXPERIENCE 4 ASSIGNMENT

  • Creating a discrete probability distribution: A venture capitalist, willing to invest $1,000,000, has three investments to choose from.

    The first investment, a social media company, has a 20% chance of returning $7,000,000 profit, a 30% chance of returning no profit, and a 50% chance of losing the million dollars.

    The second company, an advertising firm has a 10% chance of returning $3,000,000 profit, a 60% chance of returning a $2,000,000 profit, and a 30% chance of losing the million dollars.

    The third company, a chemical company has a 40% chance of returning $3,000,000 profit, a 50% chance of no profit, and a 10% chance of losing the million dollars.

    a. Construct a Probability Distribution for each investment. This should be 3 separate tables (See the instructors video for how this is done) In your table the X column is the net amount of profit/loss for the venture capitalist and the P(X) column uses the decimal form of the likelihoods given above.

    b. Find the expected value for each investment.

    c. Which investment has the highest expected return?

    d. Which is the safest investment and why?

    e. Which is the riskiest investment and why?

    When you are finished with your Assignment, upload the completed file below. You can create a spreadsheet with all of the above and submit it or create a document or write it up by hand and scan it.

  • Suppose you work for a company that manufactures electronics. The development analysts estimate that 1% of their flagship product will fail within 2 years of the purchase date, with a replacement cost of $ 1500.

    A newly hired associate at the company proposes to charge $ 6 for a 2-year warranty.

    a. Compute the expected value of this proposal. Let X be the amount profited or lost (by the company) on the warranties and P(X) is the probability. E=E=

    b. Interpret the expected value in complete sentences. (See Example 4.3 in the textbook for an example of this)

  • c. Write your review of the proposal and address it to VP of marketing and promotions. Include the following in your essay: Would the proposal benefit the company? Why or why not? Include the new proposed cost, new expected value, interpretation of the new expected value, and explanation of how the new cost was chosen.

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PRACTICE E4

  • A group of people were asked if they had run a red light in the last year. 458 responded “yes”, and 423 responded “no”.

    Find the probability that if a person is chosen at random, they have run a red light in the last year.

    Give your answer as a fraction or decimal to 4 decimal places

  • A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
  • For families with 5 children, let XX be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable XX?
  • Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
  1. The amount of rain, in inches, that will fall next Friday in Dallas, TX.
  2. The major of a randomly drawn student from Arizona State University.
  3. The number of books purchased next year by your local library.
  • i only
  • ii only
  • iii only
  • i and iii
  • ii and iii
  • i, ii, and iii

xx

P(x)P(x)

1

0.5558

2

0.034

3

0.121

4

0.3384

5

0.0378
  • yes
  • no

xx

P(x)P(x)

0

0+

1

0+

2

0+

3

0.0001

4

0.0005

5

0.0033

6

0.0155

7

0.0532

8

0.1329

9

0.2362

10

0.2835

11

0.2062

12

0.0687

Find the probability of exactly 6 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x=6)=P(x=6)=

Find the probability of 6 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x≤6)=P(x≤6)=

Does 6 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?

  • no
  • yes

Probability

Scores

0.1

2

0.5

8

0.25

9

0.05

11

0.1

13

Find the expected value of the above random variable.