Preview

Law of Averages

Good Essays
Open Document
Open Document
1479 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
Law of Averages
13. People in a large population average 60 inches tall. You will take a random sample and will be given a dollar for each person in your sample who is over 65 inches tall. For example if you sample 100 people and 20 turn out to be over 65 inches tall, you get $20. Which is better: a sample of size 100 or a sample of size 1,000? Choose one and explain. Does the law of averages relate to the answer you give?
In this case a sample size of 100 would be better. This can be explained using law of averages and also by looking at the formula for Margin of Error.
ME = 2 * SD of population/SQRT(size of sample)
In this case, the SD of population would remain the same. The only factor or value changing is the sample size. Sample size of 100 would give a bigger ME value as compared to sample size = 1000. With higher value of ME the possibility of values for height over 65 is more. However, it does not completely confirm that more values would be over 65 for sure.
Also looking at the law of averages for a sample mean, “with a large randomly selected sample, the sample average tends to be close to the true population average”. In this case it is 60 inches. “The larger the sample, closer is sample average to population average”. So if we take sample size of 1000, the average of sample would be closer to 60 inches.
Here we are assuming that the sample size of 100 and 1000 is selected without any kind of bias.
18. Based on a simple random sample of one hundred an analyst estimates the average hourly wage earned by workers in a city to be $30 and computes the margin of error to be $5. Can we conclude from this that most workers there earn between $25 and $35 an hour? Is this the right interpretation for the margin of error?
Margin of error as per the text is “it estimates the largest distance you would reasonably expect to see between sample average and population average”1. Based on the data provided above, with ME = $5 we can be confident that in the population from which

You May Also Find These Documents Helpful

  • Good Essays

    Stats Study Sheet

    • 1042 Words
    • 5 Pages

    3. A medical researcher wants to study whether oral contraceptives are correlated with high blood pressure.…

    • 1042 Words
    • 5 Pages
    Good Essays
  • Good Essays

    Confident Interval

    • 658 Words
    • 3 Pages

    inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30…

    • 658 Words
    • 3 Pages
    Good Essays
  • Good Essays

    QNT 561 Final Exam

    • 697 Words
    • 5 Pages

    11. We wish to develop a confidence interval for the population mean. The population follows the normal distribution, the standard deviation of the population is 3, and we have a sample of 10 observations. We decide to use the 90 percent level of confidence. The appropriate value of to represent the level of confidence is…

    • 697 Words
    • 5 Pages
    Good Essays
  • Good Essays

    Week Two Book Work

    • 1016 Words
    • 5 Pages

    a. Construct a 90% confidence interval for the population mean m 5 +- 1.88 b. Construct a 95% confidence interval for the population mean m 5+- 2.39 c. Construct a 99% confidence interval for the population mean m 5+- 3.75 d. Assume that the sample mean and sample standard deviation s remain exactly the same as those you just calculated but are based on a sample of n=25 observations rather than n=6 observations. Repeat parts a–c. What is the effect of increasing the sample size on the width of the confidence intervals? a)5+- 78.5 +-94.5 +-1.28 b) the sample size of the width will decrease 5.37 For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.…

    • 1016 Words
    • 5 Pages
    Good Essays
  • Satisfactory Essays

    1. Null Hypothesis Ho: u > $119,155; based on 2010 survey the average annual household income has increased.…

    • 564 Words
    • 6 Pages
    Satisfactory Essays
  • Good Essays

    Week2Assignment 322

    • 2243 Words
    • 11 Pages

    Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why? Despite, both Population A and Population having a mean height of 70.0 inches with an SD of 6.0, Population B will probably yield a more accurate estimate of its population mean. The reason for this is because Population B’s random sample of 50 people is greater than Population A’s random sample of 30 people. The additional 20 people difference in Population B allows the average amount of error of its sample means (SEM) to be smaller. The smaller the SEM, the more accurate are the sample means as estimates of the population value.…

    • 2243 Words
    • 11 Pages
    Good Essays
  • Good Essays

    Stats Study Guide

    • 789 Words
    • 4 Pages

    As reported by a recent survey, the mean height of females 20 to 29 years old is 63.6 inches. If the height is approximately normally distributed with a standard deviation of 2.8 inches,…

    • 789 Words
    • 4 Pages
    Good Essays
  • Good Essays

    Week 7 Quiz Notes

    • 2141 Words
    • 6 Pages

    A business wants to estimate the true mean annual income of its customers. The business needs to be within $250 of the true mean. The business estimates the true population standard deviation is around $2,400. If the confidence level is 90%, find the required sample size in order to meet the desired accuracy.…

    • 2141 Words
    • 6 Pages
    Good Essays
  • Good Essays

    How large was the sample? Even better, find out both the sample size and the margin of error within which the results of 95% of all samples drawn as this one was would fall.…

    • 495 Words
    • 2 Pages
    Good Essays
  • Satisfactory Essays

    Therefore, the percentage error is 1400% (rounded to significant figures) and this is a large percentage error.…

    • 164 Words
    • 1 Page
    Satisfactory Essays
  • Satisfactory Essays

    Math

    • 447 Words
    • 2 Pages

    2. A sample of 100 professors at Collin College is randomly selected. The average of their…

    • 447 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Adf-Realtes

    • 2143 Words
    • 18 Pages

    1. _____ A confidence interval for the mean of a normal population turns out to be (4.20, 7.00). The margin of error then must be (A) 5.60 (B) 2.80 (C) 11.20 (D) 1.40…

    • 2143 Words
    • 18 Pages
    Good Essays
  • Good Essays

    Survey2

    • 405 Words
    • 1 Page

    I polled a total of 16 randomly selected students from October 20th to October 24th with an outcome of 6 out of 16 (37.5%) students that approved and 10 out of 16 (62.5%) that did not approve. After collecting the data I then calculated the margin of error by using the online margin of error calculator with the population size of 29,000 and a sample size of 16 which gave me a margin of error of 24.49. Then I calculated the 95% confidence interval by adding the margin of error and the approval percentage together which gave me the maximum of the range. I continued on to find the minimum of the range by then subtracting the margin of error from the percentage approval. I then calculated a range from 13.01% to 61.99% if we expected the percentage approving to fall 95 out of 100 times. I concluded that the difference between the percentage approving and not approving is not statistically significant. Reason being is because there wasn’t enough polls to determine an accurate answer. If the sample size was greater, I believe that there would be a better chance of getting results that are more statistically significant. Thus there were some weaknesses of the poll I conducted such as the sample size. Also, the location where I conducted the survey could be a factor of a weak poll considering the huge size of the campus. Another factor that made this a weak poll was the amount of males vs females that actually had a response. Most females that I tried to survey did not have and answer which is why I have more polls of males than females. The way the question is worded can also be intimidating to people thus forcing them to give any answer instead of an accurate one. If I could change any of the factors that influence a more accurate answer, I would first of all increase the sample size to at least 1000 students. I would make sure that the amount of males and females I poll are equal. Also I would choose different sections or buildings around campus and…

    • 405 Words
    • 1 Page
    Good Essays
  • Satisfactory Essays

    variables; law of large numbers; central limit theorem; sampling distributions; tests for mean using normal…

    • 707 Words
    • 6 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Slovin Formula

    • 574 Words
    • 3 Pages

    What should be the representative sample size if the population from which the sample will be taken is 10,000 and the desired margin of error is 2%?…

    • 574 Words
    • 3 Pages
    Satisfactory Essays