Suppose that you want to estimate the mean time it takes drivers to react following the application of brakes by the driver in front of them. You take a sample of reaction time measurements and compute their mean to be 2.1 seconds and their standard deviation to be 0.5 seconds. 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 Scenario Z t could use either Z or t unclear (1) The sample has size 20, and it is from a normally distributed population with unknown standard deviation. (2) The sample has size 15, and it is from a population with a distribution about which we know very little. (3) The sample has size 95, and it is from a non-normally distributed population. (4) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 0.45. (5) The sample has size 12, and it is from a normally distributed population with a known standard deviation of 0.45.

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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Suppose that you want to estimate the mean time it takes drivers to react following the application of brakes by the driver in front of them. You take a sample of reaction time measurements and compute their mean to be

2.1

seconds and their standard deviation to be

0.5

seconds. 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 20, and it is from a normally distributed population with unknown standard deviation.
(2) The sample has size 15, and it is from a population with a distribution about which we know very little.
(3) The sample has size 95, and it is from a non-normally distributed population.
(4) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 0.45.
(5) The sample has size 12, and it is from a normally distributed population with a known standard deviation of 0.45.

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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