(Solved): The Muller-Lyer illusion is shown in the figure. Although the two horizontal lines are the same len ...

The Muller-Lyer illusion is shown in the figure. Although the two horizontal lines are the same length, the line on the left appears to be much longer. To examine the strength of this illusion, Gillam and Chambers (1985) recruited 10 participants who reproduced the length of the horizontal line in the left panel of the figure. The strength of the illusion was measured by how much longer the reproduced line was than the actual length of the line in the figure. Below are data like those observed by the researchers. Each value represents how much longer (in millimeters) the reproduced line was than the line in the figure. Estimation error: To save your time, the corresponding stats have already been calculated: $\mathrm{SS}=10.59$ and $\mathrm{M}=2.628$. Show your work (part of the steps have already been given: fill in the blanks or make your own. changes), a. Use a one-tailed hypothesis test with $?=.01$ to demonstrate that the individuals in the sample significantly overestimate the true length of the line. $p(T>)=\text{ T.DIST.RT }(,)=$ Step 4: Reject/Accept the null hypothesis. b. Calculate the estimated $d$ to measure the size of this effect. c. Construct a $95\%$ confidence interval for the population mean estimated length of the vertical line. Tip: for a $95\%$ confidence interval, use $t=\pm 2.262$, because $t^{?}2=T.INV.2T(0.05,9)=2.262$