Stat 350 Exam 2 Monday Review Solutions
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h1 Bjork Larsen needed to determine whether to use a new racing wax for the Swedish Nordic Ski Team.
He thinks that the new wax will be worth the price if it would lead to a faster race time, on average.
In the past, the average time for a standard length race was 1.40 hours.
He selects a random sample of
36 Swedish skiers and has each use the new wax system for the upcoming standard length race.
a.
Let
μ
= the average race time for all Swedish skiers using the new wax system.
State the appropriate hypotheses to be tested.
H
0
:__
μ
= 1.4
___
H
a
:__
μ
< 1.4
___
Some SPSS output based on the race times
for the 36 skiers is provided at the right and below.
b. Complete the sentence.
The histogram does not look approximately normal,
rather, it is somewhat skewed to the __
left
____.
However, the t-test result can still be considered valid
due to what main result?
The CLT or Central Limit Theorem
One-Sample Statistics
36
1.330
.124
.021
Race Time (hours)
N
Mean
Std.
Deviation
Std. Error
Mean
Race Time (hours)
1.50
1.40
1.30
1.20
1.10
1.00
Frequency
10
9
8
7
6
5
4
3
2
1
0
One-Sample Test
35
.002
-.070
-.112
-.028
Race Time (hours)
t
df
Sig.
(2-tailed)
Mean
Difference
Lower
Upper
95% Confidence
Interval of the
Difference
Test Value = 1.40
c.
What is the distribution of the test statistic if the new wax system does not
lead to faster race times
on average?
Final answer: ___
t(35) distribution
____
d.
The value of the test statistic is missing in the SPSS output. Provide its value and the corresponding
p
-value for testing the hypotheses in part (a).
p
-value = _
0.002/2 = 0.001
_____
e.
Based on the test results, which of the following is the appropriate real-world conclusion?
Clearly
circle
your answer.
i.
The new wax system significantly decreased the average race time supporting
its use by the Swedish Nordic Ski Team.
ii.
There was insufficient evidence to demonstrate the new wax system decreased the
average race time.

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