Suppose that we want to estimate the mean score on a nationwide examination in anthropology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 492 and a standard deviation of 79 . For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.(In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.) Sampling ScenarioZtcould use either Z or tunclear(1) The sample has size 75, and it is from a non-normally distributed population. (2) The sample has size 17, and it is from a normally distributed population with unknown standard deviation. (3) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 75. (4) The sample has size 19, and it is from a population with a distribution about which we know very little. (5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 75.

Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Answered: Suppose that we want to estimate the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

Suppose that we want to estimate the mean score on a nationwide examination in anthropology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of

492

and a standard deviation of

. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

(In the table,

refers to a variable having a standard normal distribution, and

refers to a variable having a t distribution.)

Sampling Scenario	Z	t	could use either Z or t	unclear
(1) The sample has size 75, and it is from a non-normally distributed population.
(2) The sample has size 17, and it is from a normally distributed population with unknown standard deviation.
(3) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 75.
(4) The sample has size 19, and it is from a population with a distribution about which we know very little.
(5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 75.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions