Previously,anorganizationreportedthatteenagersspent4.5hoursperweek,onaverage,ont

Question

Previously,anorganizationreportedthatteenagersspent4.5hoursperweek,onaverage,onthephone.Theorganization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is: a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

Explanation / Answer

Set Up Hypothesis
Null, H0: U=4.5
Alternate, H1: U>4.5
Test Statistic
Population Mean(U)=4.5
Sample X(Mean)=4.75
Standard Deviation(S.D)=2
Number (n)=15
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =4.75-4.5/(2/Sqrt(15))
to =0.484
| to | =0.484
Critical Value
The Value of |t | with n-1 = 14 d.f is 1.761
We got |to| =0.484 & | t | =1.761
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 0.4841 ) = 0.31789
Hence Value of P0.05 < 0.31789,Here We Do not Reject Ho

[ANSWER]
TYPE I ERROR:
a. to conclude that the current mean hours per week is higher than
4.5, when in fact, it is higher

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