Question

BlinkWhen two lights close together blink alternately, we “see” one light moving back and forth if the time between blinks is short. What is the longest interval of time between blinks that preserves the illusion of motion? Ask subjects to turn a knob that slows the blinking until they “see” two lights rather than one light moving. A report gives the results in the form “mean plus or minus the standard error of the mean.” Data for $12$subjects are summarized as $251\pm 45$(in milliseconds).

a. Find the sample standard deviation $S_X$for these measurements.

b. A hasty reader believes that the interval given in the report is a $95\%$confidence interval for the population mean. Find the actual confidence level for the given interval.

Short answer

a. $155.8846\mathrm{ms}$is sample standard deviation.

b.$68\%$is actual confidence level.

Step-by-step solution

Given Information

It is given that $SE=45,\overline{x}=251,n=12$

Critical value$t^{*}=1$

Confidence Level

We know that $SE=\frac{s_x}{\sqrt{n}}$

$45=\frac{s_x}{\sqrt{12}}$

$s_x=45\times \sqrt{12}$

$s_x=155.8846$

Actual Confidence Level

As it is one standard deviation, critical value $t^{\star }=1$

Degree of freedom, $df=n-1=12-1=1$

Using excel formula,$=2^{\star }TDIST(1,11,2)$, confidence level is$68\%$