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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

An example of the vertical-horizontal illusion is shown in the figure. 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 prepared an example in which both lines were exactly 10 inches long. The example was shown to individual participants who were told that the horizontal line was 10 inches long and then were asked to estimate the length of the vertical line. For a sample of n = 25 participants, the average estimate was M = 12.2 inches with a standard deviation of s = 1.00.

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

b. Calculate the estimated d and r2, the percentage of variance accounted for, to measure the size of this effect.

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

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a.

To determine

To Find: If the individuals in the sample significantly overestimate the true length of the line using one-tailed test with α=0.01

Explanation

Given info:

A sample of 25 individual is selected from a population with mean 10. The sample mean,  and standard deviation (s) are 12.2 and 1 respectively. One-tailed hypothesis test using α=0.01 is to be performed.

Calculations:

Step 1: Null Hypothesis is H0:μ10 and Alternate Hypothesis is H1:μ>10

Step 2: For a sample of n=25 , the t-statistics will have (n1) degrees of freedom, i.e. df=24 . For a one-tailed test with α=0.01 and df=24 , the critical value (CV)  is obtained from the t-table as t=2.492

Step 3: t-statistics can be calculated using formula:

t=Mμsm

Calculate sm using the formula:

sm=sn=125=15=0

b.

To determine

To Find: The Cohen’s d and r2 for the given question.

b.

To determine

To Find: Make a 95% confidence interval estimate for the given question

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