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.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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