Answered: Recall that a tt-distribution has…

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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Recall that a tt-distribution has "fatter tails" than a normal distribution, so that a higher proportion of the tt-distribution is in the tails, and a smaller proportion is in the middle.

a)If we mistakenly used the z-distribution instead of t-distribution when performing a hypothesis test for a mean, what would happen to our P-value?

Choice 1 of 3:The P-value calculated from the Z-distribution would be larger than the P-value from the t-distribution.

Choice 2 of 3:The P-value calculated from the Z-distribution would be smaller than the P-value from the t-distribution.

Choice 3 of 3:The P-values from the two distributions would be about the same.

b)If we mistakenly use the Z-distribution instead of a t-distribution when performing a hypothesis test for a mean, how does this affect how likely we are to reject the null hypothesis amd why?

Choice 1 of 3:We are more likely to reject the null hypothesis when using the Z-distribution than we are with the t-distribution.

Choice 2 of 3:We are less likely to reject the null hypothesis when using the Z-distribution than we are with a t-distribution.

Choice 3 of 3:We are equally likely to reject in both situations.

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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