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Lecture

MATH 1P98 Lecture Notes - Null Hypothesis, Statistical Hypothesis Testing


Department
Mathematics and Statistics
Course Code
MATH 1P98
Professor
Dot Miners

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Confidence intervals & proportions
Margin of error: E = zc
p̂
1q̂
1
n1
+p̂
2q̂
2
n2
Hypothesis testing
Ex: A car manufacturer states that its new model gets 78mi/gal
Let µ be the mean gas mileage for this car. Manufacturer may overvalue car.
The claim µ = 47 is called the Null Hypothesis. (H0: µ = 47)
If I reject the null hypothesis, I need a claim to accept; the Alternate Hypothesis.
Alternate hypothesis is that µ < 47. (H1: µ < 47)
Types of tests
Left tailed: if H1 states that the parameter is less than the value claimed in H0.
Right tailed: if H1 states that the parameter is more than the value claimed in H0.
Two tailed: if H1 states that the parameter is different than the value claimed in H0.
Ex: Rosie the sheepdog. Vet fears her heart rate is slowing. For this breed:
µ = 115bpm σ = 12bpm
The vet takes Rosie’s pulse 6 times in 6 weeks.
x = 105bpm̄
H0: µ = 115bpm
H1: µ < 115bpm
How do we test this?
z =
̄
xµ
σ
n
; z =
105115
12
6
; z = -2.04
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