Download Testing Hypothesis with Small Samples

Testing Means with small samples
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Critical Value from the T-table
– Use the one-tail heading for left or right tail
• Make negative for left-tail
– Use the two-tails heading for two tailed test
– Remember degrees of freedom
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For Example
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4.
H0: μ ≥ 25, n = 18, Degree of confidence = 99%
H0: μ = 110, n = 25, Degree of confidence = 95%
H0: μ ≤ 1.5, n = 12, Degree of confidence = 90%
H0: μ = 74, n = 28, Degree of confidence = 99.9%
Live example/Your Turn
• What would you guess to be average age of South
students’ cars?
– Let’s do a survey!!
• What would you guess to be minimum number of
colleges that average South student’s applied to?
– Let’s take a sample!!
Worksheet
Sample mean =
Original claim
Opposite claim
Degree of confidence
Test statistics
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
n=
s=
•Label null and
alternative
hypothesis
Worksheet
Sample mean =
Original claim
Opposite claim
Degree of confidence
Test statistics
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
n=
s=
•Label null and
alternative
hypothesis
Testing Hypothesis with Small Samples
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We use the T (Student) table (A-3) to find the critical value
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We need to know the degrees of freedom, the significance level
(alpha), and the number of tails
Calculator:
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[STAT]
TESTS
1: T-Test…
• μ0 is the benchmark.
• X-bar is the mean
• Sx is the standard deviation
• n is the sample size
• μ select the format of H1
Homework: Test the claims
1.
2.
3.
4.
5.
Claim: Student population has a mean GPA of 2.0. A sample of 24
students has a mean is 2.35 and a standard deviation is 0.70. Use a
95% degree of confidence
Claim: An SAT prep class produces scores above 1700. A sample
of 15 students has a mean is 1685 and a standard deviation is 170.
Use a 99% degree of confidence
Claim: The average college student needs at least 5 years to get a
degree. A sample of 20 students has a mean of 5.15 years and the
standard deviation is 1.68. Use a 90% degree of confidence
The following list contains the repair costs for five BMW cars
used in a controlled crash test: 797 571 904 1147 418. Use this
sample to text the claim that BMW’s repair costs are under $1000.
Using a sample of 25 adults whose mean body temperature was
98.24 (standard deviation = 0.56), Test the claim that the mean
body temperature for the population is 98.6
Homework #1
Sample mean = 2.35
n = 24
s = 0.07
Original claim
µ = 2.0 (H0)
Opposite claim
µ ≠ 2.0 (H1)
Label null and
alternative
hypothesis
Degree of confidence
95%
Test statistics
t = 2.45
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
p-value = 0.022 < 0.05
Reject null, reject original claim
Homework #2
Sample mean = 1685
n = 15
s = 170
Original claim
µ > 1700 (H0)
Opposite claim
µ ≤ 1700 (H1)
Label null and
alternative
hypothesis
Degree of confidence
99%
Test statistics
t = -0.342
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
p-value = 0.631 > 0.01
FRT null, FTR original claim
Homework #3
Sample mean = 5.15
n = 20
s = 1.68
Original claim
µ ≥ 5(H0)
Opposite claim
µ < 5 (H1)
Label null and
alternative
hypothesis
Degree of confidence
90%
Test statistics
t = 0.399
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
p-value = 0.653 > 0.1
FRT null, FRT original claim
Homework #4
Sample mean = 588
n=5
s = 424
Original claim
µ < 1000 (H1)
Opposite claim
µ ≥ 1000 (H0)
Label null and
alternative
hypothesis
Degree of confidence
95%
Test statistics
t = -2.17
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
p-value = 0.048 < 0.05
Reject null, accept original claim
Homework #5
Sample mean = 98.24
n = 25
s = 0.56
Original claim
µ = 98.6 (H0)
Opposite claim
µ ≠ 98.6 (H1)
Label null and
alternative
hypothesis
Degree of confidence
95%
Test statistics
t = -3.214
Critical region
•Two-tailed (H0 =)
•Left tailed (H0 )
•Right tailed (H0 )
Critical value
Reject or accept?
p-value = 0.0037 < 0.05
Reject null, reject original claim