**Confidence Intervals and Population Mean Estimation**You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose, we choose a random sample of exam scores. The sample we choose has a mean of 511 and a standard deviation of 71.### Question (a)**(a) What is the best point estimate, based on the sample, to use for the population mean?***Answer Placeholder:* [ ]### Question (b)**(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean.***(In the table, Z refers to a standard normal distribution, and t refers to a t-distribution.)***Note:** There is a graphical element with three icons (a cancel X, a refresh arrow, and a question mark) likely intended as interactive elements for user responses.For further details on creating confidence intervals and understanding different sampling scenarios, refer to the linked resources in each associated term.**Keywords Explained**- **Confidence Interval:** A range of values used to estimate a population parameter.- **Population Mean:** The average of a set of measurements in the entire population.- **Random Sample:** A subset of individuals chosen from a larger set, where each individual is chosen randomly.- **Standard Deviation:** A measure of the amount of variation or dispersion in a set of values.- **Critical Value:** The value that a test statistic must exceed for the null hypothesis to be rejected in a hypothesis test.- **Standard Normal Distribution (Z):** A normal distribution with a mean of 0 and a standard deviation of 1.- **t Distribution:** A type of probability distribution that is symmetric and bell-shaped but has heavier tails than the standard normal distribution.By understanding these fundamental concepts, you can effectively calculate confidence intervals and use appropriate distributions for statistical estimations, crucial skills in data analysis and interpretation. **Table: Choosing Between Z and t Distributions in Different Sampling Scenarios**This table presents different sampling scenarios and indicates whether the Z distribution, t distribution, or either could be used, or if the situation is unclear.| Sampling scenario | Z | t | Could use either Z or t | Unclear ||-----------------------------------------------------------------------------------------------------------|-----|-----|-------------------------|---------|| The sample has size 19, and it is from a normally distributed population with an unknown standard deviation. | | • | | || The sample has size 85, and it is from a non-normally distributed population. | | | | • || The sample has size 110, and it is from a non-normally distributed population with a known standard deviation of 76. | • | | | |In each row, the respective circles (•) denote the appropriate choice for the sampling scenario described. Specifically:- For a sample size of 19 from a normally distributed population with an unknown standard deviation, the t distribution is appropriate.- For a sample size of 85 from a non-normally distributed population, it is unclear whether to use Z or t.- For a sample size of 110 from a non-normally distributed population with a known standard deviation of 76, the Z distribution is appropriate.

Given: Sample mean is 511 Sample standard deviation is 71

Answered: You would like to construct a 95%…

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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