Homework Answers
a) point estimate = x̅ = ΣX/n = 20.78
b) sample std dev , s = √(Σ(X- x̅ )²/(n-1) )
= 15.4364
Sample Size , n = 40
Level of Significance , α =
0.05
degree of freedom= DF=n-1= 39
't value=' tα/2= 2.0227 [Excel
formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 15.4364 /
√ 40 = 2.4407
margin of error , E=t*SE = 2.0227
* 2.4407 = 4.9368
c)
confidence interval is
Interval Lower Limit = x̅ - E = 20.78
- 4.9368 = 15.8382
Interval Upper Limit = x̅ + E = 20.78
- 4.9368 = 25.7118
95% confidence interval is (
15.84 < µ < 25.71
)
d)
skewness=n/((n-1)(n-2))[Σ((X-mean)/s)³= 0.5861
considering a slightly larger sample next time is a good strategy
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