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.

Step by step solution

01

Given Information

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

Critical value$t^{*}=1$

02

Confidence Level

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

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

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

$s_x=155.8846$

03

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$68\%$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!