Ability to concentrate can be measured by perception of time. In a study, twenty

Question

Ability to concentrate can be measured by perception of time. In a study, twenty people were told when a 45-second period started and stopped. They were then asked how much time they thought had elapsed. The following data shows their perception of the time that had passed in seconds. Conduct a hypothesis test to determine if these data provide evidence that their perception of time elapsed differs from 45 seconds, the actual time that had elapsed. Use a significance level of 0.05.

69 65 72 73 59 55 39 52 67 57

56 50 70 47 56 45 70 64 67 53

Explanation / Answer

Set Up Hypothesis
Null, H0: U=45
Alternate,perception of time elapsed differs from 45 seconds H1: U!=45
Test Statistic
Population Mean(U)=45
Sample X(Mean)=59.3
Standard Deviation(S.D)=9.836
Number (n)=20
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =59.3-45/(9.836/Sqrt(20))
to =6.502
| to | =6.502
Critical Value
The Value of |t | with n-1 = 19 d.f is 2.093
We got |to| =6.502 & | t | =2.093
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 6.5018 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

We have evidence that perception of time elapsed differs from 45 seconds

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