Question

1. Independent t-Test: A researcher examines the short-term effect of a single treatment with acupuncture on cigarette smoking. Subjects who smoke ~ 1 ppd are assigned to one of two groups. One group (M₂) receives acupuncture the second is a control group (M₁) with no acupuncture. The number of cigarettes smoked the next day is recorded. You want to know if acupuncture will decrease cigarette smoking with alpha level of .05.
   

n= 8     M₁ = 20.5        M₂= 11.125     S²₁= 34.29       S²₂=57.84

1. State you null and alternative hypothesis
2. Find your critical region
3. Calculate F-max
4. Conclusion?
5. Calculate t

Conclusion?

Answer 1

a) Null and alternative hypotheses

Ho:  1 = 2

H1:  1 > 2

b) For a = 0.05 and d.f = n1+ n2 -2

d.f = 8 + 8 -2 = 14

tcritical = t_{​​​​​​a , d.f} = t_{​​​​​​0.05 , 14}

tcritical = 1.761

c) F max = S_{​​​​​​2}^{​​​​2}​/S_{​​​​1}²

F max = 57.84/34.29

F max = 1.69

d) if t > 1.761 ,we reject the null hypothesis otherwise we fail to reject the null hypothesis.

e). t = M1 - M2/ Sp * sqrt(1/n1+1/n2)

Sp = sqrt((n1-1)s12 + (n2-1)s22)/n1+n2-2))

Sp = 6.79

t = 20.5 - 11.125/6.79*0.5

t = 2.76

Here t = 2.76 > 1.69 , so we reject the null hypothesis.

Conclusion : There is sufficient evidence to support the claim accupuncture treatment decreases cigarette smoking