# 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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A company is started by four friends. The company was Erica’s idea, so she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. What is the name of the appropriate inference procedure? chi-square test for goodness of fit one-sample t-test for a difference in means two-sample t-test for a difference in means two-sample z-test for a difference in proportions
Someone claims that, since the mean of the sampling distribution equals the population mean, any single sample mean must also equal the population mean. Explain?
Prof. Jacob wants to know, with 90% confidence, the proportion of students who like to eat in the cafeteria. A previous survey showed that 62% like to eat in the cafeteria. Prof. Jacob likes to be accurate with an error of 0.025 of its true proportion. What sample size does Prof. Jacob need?* A. 1,020 B. 1,020.06 C. 1,021 D. 1,022
The large airline company, Tale Winds, knows from experience that only 77% of the passengers booked for flights actually show up. Suppose that we will take a random sample of 8 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 un (the mean of the sampling distribution of the sample proportion). HA = ] (b) Find oA (the standard deviation of the sampling distribution of the sample proportion). ? Continue Submit Assignment O 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility APR ?? 6. étv MacBook Air 80 DI DD F3 F4 F5 F6 F7 FB F9 F10 F11 F12 %24 & 3 5 6 9. delete %3D
I. Direction: Construct the sampling distribution of the sample means and answer the questions that follow: 1. A jar contains numbers 0, 1, 2 and 3. Construct the sampling distribution of the sample means when two numbers are taken from the jar with replacement a. what is the probability that the mean of the numbers is 1.5 ? b. what is the probability that the mean of the numbers is less than 12 c. what is the probability that the mean of the numbers is greater than 0.52 d. what is the probability that the mean of the numbers is between 1.5 and 3. e. construct the histogram of the sampling distribution
What is the shape of the sampling distribution?
Make your own example of mean of a sampling distribution. Also, construct the sampling distribution.
Race organizers want to survey the participating runners on the quality of the running course. Which of the following uses systematic random sampling? Select the first 15 finishers and the last 15 finishers to take the survey. Randomly select 15% of the male participants and 15% of the female participants. Select the 5th finisher (with the number 5 being randomly chosen) to survey, then survey every 15th finisher after that. Sort all of the runners' names alphabetically, then randomly choose 2 letters and survey all participants whose last name begins with one of those letters.
For a large, top-rated corporation, 91% of employees said the corporation is a great place to work. Suppose that we will take a random sample of 10 employees. Let p represent the proportion of employees from the sample who said the corporation is a great place to work. 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 n (the mean of the sampling distribution of the sample proportion). ? (b) Find on (the standard deviation of the sampling distribution of the sample proportion). ?
What is the mean of the sampling distribution? (round to 3 decimal places)
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…

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