Answer:
see explaination
Step-by-step explanation:
Data : 32.1 , 30.6 , 31.4 , 30.4 , 31.0 , 31.9
Mean X-bar = 31.23
SD = 0.689
a)
Null Hypothesis : Xbar = mu
Alternate Hypothesis : Xbar > mu
z = (Xbar - mu) / (SD/sqrt(n))
= (31.23 - 30 ) /(0.689/sqrt(6))
= 4.372
P-value = ~0
Since P-vale < 0.01 , we will reject null hypothesis.
The data suggest that true average stopping ditance exceeds the maximum.
b)
i) SD = 0.65
mu = 31
z = (Xbar - mu) / (SD/sqrt(n))
= (31.23 - 31) /(0.65/sqrt(6))
= 0.867
P-value = 0.3859 Answer
ii) SD = 0.65
mu = 32
z = (Xbar - mu) / (SD/sqrt(n))
= (31.23 - 32) /(0.65/sqrt(6))
= -2.9
P-value = 0.0037 Answer
c)
i) SD = 0.8
mu = 31
z = (Xbar - mu) / (SD/sqrt(n))
= (31.23 - 31) /(0.8/sqrt(6))
= 0.704
P-value = 0.4814 Answer
ii) SD = 0.8
mu = 32
z = (Xbar - mu) / (SD/sqrt(n))
= (31.23 - 32) /(0.8/sqrt(6))
= -2.357
P-value = 0.0184 Answer
The probabilities obtained in part c are comparatively higher than that of part b.
d)
i) For alpha =0.01
z = (Xbar - mu) / (SD/sqrt(n))
=> -2.32 = (31.23 - 31) /(0.65/sqrt(n))
=> (0.65/sqrt(n)) = (31.23 - 31)/-2.32
=> sqrt(n) = (0.65*(-2.32)) / (31.23 - 31)
=> n = 43 Answer
ii) For beta =0.10
z = (Xbar - mu) / (SD/sqrt(n))
=> -1.28 = (31.23 - 31) /(0.65/sqrt(n))
=> (0.65/sqrt(n)) = (31.23 - 31)/-1.28
=> sqrt(n) = (0.65*(-1.28)) / (31.23 - 31)
=> n = 13 Answer
r^2*h/3