Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepares an example in which both lines are exactly 10 inches long. The example is shown to individual participants who are told that the horizontal line is 10 inches long and then are asked to estimate the length of the vertical line. For a sample of n = 25 participants, the average estimate is M = 12.2 inches with a standard deviation of s = 1.00. Use a one-tailed hypothesis test with α = .01 to demonstrate that the individual participants in the sample significantly overestimate the true length of the line. (Note: Accurate estimation would produce a mean μ = 10 inches.) (Use three decimal places.) t-critical = t = The results indicate: Failure to reject the null hypothesis; there is not significant evidence that the true length of the vertical line is overestimated Failure to reject the null hypothesis; there is significant evidence that the true length of the vertical line is overestimated Rejection of the null hypothesis; there is significant evidence that the true length of the vertical line is overestimated Rejection of the null hypothesis; there is not significant evidence that the true length of the vertical line is overestimated

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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Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepares an example in which both lines are exactly 10 inches long. The example is shown to individual participants who are told that the horizontal line is 10 inches long and then are asked to estimate the length of the vertical line. For a sample of n = 25 participants, the average estimate is M = 12.2 inches with a standard deviation of s = 1.00.

Use a one-tailed hypothesis test with α = .01 to demonstrate that the individual participants in the sample significantly overestimate the true length of the line. (Note: Accurate estimation would produce a mean μ = 10 inches.) (Use three decimal places.)

t-critical	=
t	=

The results indicate:

Failure to reject the null hypothesis; there is not significant evidence that the true length of the vertical line is overestimated

Failure to reject the null hypothesis; there is significant evidence that the true length of the vertical line is overestimated

Rejection of the null hypothesis; there is significant evidence that the true length of the vertical line is overestimated

Rejection of the null hypothesis; there is not significant evidence that the true length of the vertical line is overestimated

Calculate the estimated Cohen’s d and r², the percentage of variance accounted for, to measure the size of this effect. (Use four decimal places.)

d	=
r²	=

Construct a 95% confidence interval for the population mean estimated length of the vertical line:

12.000 to 12.400

11.787 to 12.613

10.136 to 14.264

10.962 to 13.438

Expert Solution

Step 1

Note: We'll answer the first question since the exact one wasn't specified. Please submit a new question specifying the one you'd like answered.

Given:

n = 25

$X$ = 12.2

s = 1

$α$ = 0.01

Formula Used:

t-test = $\frac{X - μ}{\frac{s}{\sqrt{n}}}$

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