# Exploring Sampling Distributions### Question (b)**Scenario:**What would the sampling distribution of the sample mean for a random sample of size \( n = 9 \) policy holders look like?**Interaction:**- A blank graph area is provided with the option to "Choose one" from different sampling distribution options.- Users have control buttons at the bottom to interact with: - A play button (probably to simulate or animate the sampling process) - A calculator icon (potentially to perform computations) - A slider to choose between distribution options or scenarios.- There are three buttons at the top-right for various actions: - An X button (possibly to exit or clear the selection) - A reset button (to undo actions) - A question mark (for help or information)### Question (c)**Scenario:**What would the sampling distribution of the sample mean for a random sample of size \( n = 32 \) policy holders look like?**Interaction:**- Another blank graph area with similar interaction options as above for choosing or simulating the sampling distribution.- Includes the same control buttons for interaction, suggesting similar functionalities.**Overview:**These interactive components aim to help students understand how sampling distributions change with different sample sizes. By engaging with these options, learners can observe concepts such as variability, central tendency, and the central limit theorem in action. ### Overview of Homeowner's Insurance Claims DistributionOver the lifetime of a certain company’s homeowners insurance policy, the number of claims filed by the holder has a population distribution, as depicted in the histogram below. The population mean is also provided.#### Histogram Explanation- **Title:** Population- **Axes:** - **Vertical Axis (Y-axis):** Represents Probability. - **Horizontal Axis (X-axis):** Represents the Number of claims.- **Bars:** - Range from 0 to 3 claims. - The probability for each number of claims: - 0 claims: ~0.1 probability - 1 claim: ~0.3 probability - 2 claims: ~0.3 probability - 3 claims: ~0.2 probability- **Population Mean:** μ = 1.5 (indicated on the right side of the graph)### Sampling Distribution Question(a) What would the sampling distribution of the sample mean for a random sample of size \( n = 3 \) policyholders look like? Use the slider to select the best answer.(Note: The interaction asks for using a slider to choose an answer, which suggests an interactive tool is provided for exploration of sampling distributions based on sample size.)

Answered: Image /qna-images/answer/6852a3d3-18cf-46d2-bdfe-fdac0c6d3fec.jpg

Answered: (b) What would the sampling…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll an eight-sided die two times (or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4, 5, 6, 7, and 8. The true mean (µ) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 is , and the true standard deviation (o) is The number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (8) times the number of possibilities on the second roll (also 8), or 8(8) = 64. If you collected all of these possible samples, the mean of your sampling distribution of means (µM) would equal and the standard deviation of your sampling distribution of means (that is, the standard error or ɑm) would be The following chart…
You want to get a probability-based sample to gauge freshmen opinion about the food served on campus. Give three different probability-based sampling strategies (simple random, systemic, and stratified). How would you design your data collection strategy for each of three methods? What type of sampling frame might you need for this work?
A researcher wants to study the effects of social media on Grade 11 students in Mathematics High School. He wishes to use the simple random sampling technique in choosing the members of his sample. If there are 1,000 Grade 11 students in the school, how many students should there be in his sample? Discuss the steps he must take if he wishes to use the lottery method.
Knowing that you need a sample pool of 536 students to ultimately get about 250 students in your sample, you are in position to draw a systematic sample from the student directory at your university. Further, 5,000 students are listed in the directory. What is the sampling interval?
Suppose you recruit the next 100 people who visit the DCC cafeteria to participate in a survey. One of the questions you ask is whether the student eats on campus (i.e., in the cafeteria) regularly, and you want to use the sample proportion to estimate the value of the (population) proportion of all DCC students who eat on campus regularly. Do you think this sampling method is likely to be biased? If so, in which direction? This sampling method is not likely to be biased and will produce a representative sample of DCC students. This sampling method is biased and is likely to yield an overestimate for the population proportion. This sampling method is biased and is likely to yield an underestimate for the population proportion.
can you help for answer this ?
Q. Illustrate different types of sampling (Probability & Non Probability) with real life examples.
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The large airline company, Tale Winds, knows from experience that only 73% of the passengers booked for flights actually show up. Suppose that we will take a random sample of 7 Tale Winds passengers. Let p represent the proportion of passengers from the sample who show up for their flight. Consider the sampling distribution of the sample proportion p. Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed. (a) Find la (the mean of the sampling distribution of the sample proportion). Hn =| ? p (b) Find on (the standard deviation of the sampling distribution of the sample proportion). on = | ?
According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was Hispanic: 28% Black: 24% White: 35% Asian: 12% Others: 1% The manager of a large housing complex in the city wonders whether the distribution by race of the complex’s residents is consistent with the population distribution. To find out, she records data from random sample of 800 residents. The table below displays the sample data. Race Hispanic Black White Asian Others Count 212 202 270 94 22 Are these data significantly different from the city’s distribution by race? Carry out an appropriate test at the ? = 0.05 level of significance to support your answer. State the null and alternate hypotheses (write it mathematically) and write your claim. Find the test statistics. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical…
In each situation, find the value of the standardized statistic for the sample mean, and indicate whether the standardized statistic is a t-statistic or a z-statistic. (Round your answer for part (a) to three decimal places.) (a) x = 195, u= 190, s = 21, n = 4 standardized statistic = it's t because s is used instead of o v (b) x = 195,H= 190, o = 25, n = 4 standardized statistic = it's z because o is known (c) x = 168,H= 190, s = 22, n = 25 standardized statistic = : it's t because s is used instead of o
A choral conductor has 1885 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1885, so she instead asks 630 singers in front and finds 17 who are professionals. (a) Identify the sample.A. 17/1885B. 630C. singers who were askedD. None of the above. (b) Identify the populationA. percentage of entire singers who are professionalB. entire singersC. 17/1885D. None of the above. (c) What specific type of bias does this scenario demonstrate?A. Voluntary response samplingB. Convenience SamplingC. It is representative of the population.D. None of the above. (d) Identify the parameterA. range of values in which 95% values fallB. percentage of entire singers who are professionalC. 17D. None of the above.

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