Consider the following Minitab output Test and CI for One Pr

Consider the following Minitab output. Test and CI for One Proportion is this a one-sided or a two-sided test? Was this test conducted using the normal approximation to the binomial? Was that appropriate? Fill in the missing values.

Solution

Q1.

Set Up Hypothesis
Null, H0:P=0.65
Alternate, H1: P>0.65
Test Statistic
No. Of Success chances Observed (x)=553
Number of objects in a sample provided(n)=800
No. Of Success Rate ( P )= x/n = 0.6913
Success Probability ( Po )=0.65
Failure Probability ( Qo) = 0.35
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.69125-0.65/(Sqrt(0.2275)/800)
Zo =2.45
P-Value: Right Tail - Ha : ( P > 2.44612 ) = 0.00722

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=553
Sample Size(n)=800
Sample proportion = x/n =0.691
Confidence Interval = [ 0.691 ±Z a/2 ( Sqrt ( 0.691*0.309) /800)]
= [ 0.691 - 1.96* Sqrt(0) , 0.691 + 1.96* Sqrt(0) ]
= [ 0.659,0.723]

ANS.
a) One sided
Reason : Hypothesis is defined to right tailed H0:P=0.65, H1: P>0.65
b)
No
c)
Sample p = 0.691,
Lower Bound = 0.659
P-Value: Right Tail - Ha : ( P > 2.44612 ) = 0.00722