SFU Stat Normal Distributions Questions
The Six StepsStep 1
Null Hypothesis
Alternative Hypothesis
H0 :
HA :
Step 2
The t-statistic:
x!µ
t-statistic = p
s/ n
Since the histogram suggests that the data are normally distributed, the t
statistic has a Student-t distribution. Critical value can be obtained from
the Student t-table.
Step 3
! = 0.05
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Step 4 Decision Rule.
Reject H0 if t < !t!,n!1 = !t0.05,50!1 = !1.676 (use d.f. = 50).
Step 5 Value of the test statistic:
(i) Solving by hand.
From the histogram, x̄ = 11.744 and s = 2.042. Thus
t =
x!µ
ps
n
=
11.744 ! 12
2.042
p
50
= !0.886
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(ii) Using the computer.
EViews Commands. To carry out the t-test, click on the View button, then
choose Descriptive Statistics & tests / Simple Hypothesis Tests. Type in
the value of "12" in the edit box next to the Mean.
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EViews Output
The EViews output also shows that t = !0.886.
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Step 6.
Since t = !0.886 > !t0.05,50!1 = !1.676, we fail to reject H0.
There is (evidence, not enough evidence) to claim that the owner’s claim —
that the average waiting time is less than its advertised time of 12 minutes
— is true.
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