#### Transcript 4.3

```Section 4.3
Determining
Statistical Significance
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Review
The smaller the p-value the
a) stronger the evidence against the null hypothesis
b) stronger the evidence for the null hypothesis
If the p-value is low, then it would be very rare
to get results as extreme as those observed, if
the null hypothesis were true. This suggests
that the null hypothesis is probably not true!
Statistics: Unlocking the Power of Data
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Red Wine and Weight Loss
• Resveratrol, an ingredient in red wine and
grapes, has been shown to promote weight loss
in rodents, and has recently been investigated in
primates (specifically, the Grey Mouse Lemur).
• A sample of lemurs had various measurements
taken before and after receiving resveratrol
supplementation for 4 weeks
BioMed Central (2010, June 22). “Lemurs lose weight with
‘life-extending’ supplement resveratrol. Science Daily.
Statistics: Unlocking the Power of Data
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Red Wine and Weight Loss
In the test to see if the mean resting metabolic
rate is higher after treatment, the p-value is 0.013.
Using  = 0.05, is this difference statistically
significant? (should we reject H0?)
a) Yes
b) No
The p-value is lower than
 = 0.05, so the results
are statistically significant
and we reject H0.
Statistics: Unlocking the Power of Data
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Red Wine and Weight Loss
In the test to see if the mean body mass is lower
after treatment, the p-value is 0.007.
Using  = 0.05, is this difference statistically
significant? (should we reject H0?)
a) Yes
b) No
The p-value is lower than
 = 0.05, so the results
are statistically significant
and we reject H0.
Statistics: Unlocking the Power of Data
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Red Wine and Weight Loss
In the test to see if locomotor activity changes
after treatment, the p-value is 0.980.
Using  = 0.05, is this difference statistically
significant? (should we reject H0?)
a) Yes
b) No
The p-value is not lower
than  = 0.05, so the
results are not statistically
significant and we do not
reject H0.
Statistics: Unlocking the Power of Data
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Red Wine and Weight Loss
In the test to see if mean food intake changes
after treatment, the p-value is 0.035.
Using  = 0.05, is this difference statistically
significant? (should we reject H0?)
a) Yes
b) No
The p-value is lower than
 = 0.05, so the results
are statistically significant
and we reject H0.
Statistics: Unlocking the Power of Data
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Statistical Conclusions
In a hypothesis test of
H0:  = 10 vs Ha:  < 10
the p-value is 0.002. With α = 0.05, we conclude:
a) Reject H0
b) Do not reject H0
c) Reject Ha
The p-value of 0.002
is less than α = 0.05,
so we reject H0
d) Do not reject Ha
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Statistical Conclusions
In a hypothesis test of
H0:  = 10 vs Ha:  < 10
the p-value is 0.002. With α = 0.01, we conclude:
a) There is evidence that  = 10
b) There is evidence that  < 10
c) We have insufficient evidence to conclude anything
Statistics: Unlocking the Power of Data
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Statistical Conclusions
In a hypothesis test of
H0:  = 10 vs Ha:  < 10
the p-value is 0.21. With α = 0.01, we conclude:
a) Reject H0
b) Do not reject H0
c) Reject Ha
d) Do not reject Ha
Statistics: Unlocking the Power of Data
The p-value of 0.21 is
not less than α =
0.01, so we do not
reject H0
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Statistical Conclusions
In a hypothesis test of
H0:  = 10 vs Ha:  < 10
the p-value is 0.21. With α = 0.01, we conclude:
a) There is evidence that  = 10
b) There is evidence that  < 10
c) We have insufficient evidence to conclude anything
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How many of the following p-values are
significant at the 5% level?
0.005
A. 1
0.03
B. 2
0.08
C. 3
0.42
0.79
D. 4
E. 0 or 5
Two of the p-values
are less than 0.05 so
are significant at a 5%
level.
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How many of the following p-values are
significant at the 10% level?
0.005
A. 1
0.03
B. 2
0.08
C. 3
0.42
0.79
D. 4
E. 0 or 5
Three of the p-values
are less than 0.10 so
are significant at a
10% level.
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How many of the following p-values are
significant at the 1% level?
0.005
A. 1
0.03
B. 2
0.08
C. 3
0.42
0.79
D. 4
E. 0 or 5
Only one of the p-values
is less than 0.01 so only
one is significant at a 1%
level.
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A new blood thinning drug is being tested against
the current drug in a double-blind experiment. Is
there evidence that the mean blood thinness rating
is higher for the new drug? Using n for the new
drug and o for the old drug, which of the following
are the null and alternative hypotheses?
A.
B.
C.
D.
E.
H0: n > o vs Ha: n = o
H0: n = o vs Ha: n  o
H0: n = o vs Ha: n > o
H0: xn  xo vs Ha: xn  xo
H0: xn  xo vs Ha: xn  xo
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A new blood thinning drug is being tested
against the current drug in a double-blind
experiment, and the hypotheses are:
H0: n = o vs Ha: n > o
What does a Type 1 Error mean in this situation?
A. We reject H0
B. We do not reject H0
C. We find evidence the new drug is better
when it is really not better.
D. We are not able to conclude that the new
drug is better even though it really is.
E. We are able to conclude that the new drug is
better.
Statistics: Unlocking the Power of Data
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A new blood thinning drug is being tested against
the current drug in a double-blind experiment,
and the hypotheses are:
H0: n = o vs Ha: n > o
What does a Type 2 Error mean in this situation?
A. We reject H0
B. We do not reject H0
C. We find evidence the new drug is better when
it is really not better.
D. We are not able to conclude that the new drug
is better even though it really is.
E. We are able to conclude that the new drug is
better.
Statistics: Unlocking the Power of Data
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A new blood thinning drug is being tested
against the current drug in a double-blind
experiment, and the hypotheses are:
H0: n = o vs Ha: n > o
If the new drug has potentially serious side
effects, we should pick a significance level that
is:
A. Relatively small (such as 1%)
B. Middle of the road (5%)
C. Relatively large (such as 10%)
Since a Type 1 error would be
serious, we use a small significance
level.
Statistics: Unlocking the Power of Data
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A new blood thinning drug is being tested
against the current drug in a double-blind
experiment, and the hypotheses are:
H0: n = o vs Ha: n > o
If the new drug has no real side effects and
costs less than the old drug, we might pick a
significance level that is:
A. Relatively small (such as 1%)
B. Middle of the road (5%)
C. Relatively large (such as 10%)
Since a Type 1 error is not at all
serious here, we might use a large
significance level.
Statistics: Unlocking the Power of Data
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