Consider the following hypotheses Compute the pvalue based o

Consider the following hypotheses:

Compute the p-value based on the following sample information. Use Table 1. (Round intermediate calculations to 4 decimal places. Round \"z\" value to 2 decimal places and final answers to 4 decimal places.)

a.

x = 31; n = 86

  

Consider the following hypotheses:

H0: p ? 0.44

HA: p < 0.44

Compute the p-value based on the following sample information. Use Table 1. (Round intermediate calculations to 4 decimal places. Round \"z\" value to 2 decimal places and final answers to 4 decimal places.)

Consider the following hypotheses: H0: p ? 0.44 HA: p

Solution

a)
Test Statistic
No. Of Success chances Observed (x)=31
Number of objects in a sample provided(n)=86
No. Of Success Rate ( P )= x/n = 0.3605
Success Probability   ( Po )=0.44
Failure Probability ( Qo) = 0.56
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.36047-0.44/(Sqrt(0.2464)/86)
Zo =-1.4859
P-Value: Left Tail -Ha : ( P < -1.48589 ) = 0.06865
b)
Test Statistic
No. Of Success chances Observed (x)=114
Number of objects in a sample provided(n)=326
No. Of Success Rate ( P )= x/n = 0.3497
Success Probability   ( Po )=0.44
Failure Probability ( Qo) = 0.56
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.34969-0.44/(Sqrt(0.2464)/326)
Zo =-3.2848
P-Value: Left Tail -Ha : ( P < -3.2848 ) = 0.00051

c)
No. Of Success Rate ( P )= x/n = 0.34
Success Probability   ( Po )=0.44
Failure Probability ( Qo) = 0.56
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.34-0.44/(Sqrt(0.2464)/65)
Zo =-1.6242
P-Value: Left Tail -Ha : ( P < -1.62419 ) = 0.05217

d)
Success Probability   ( Po )=0.44
Failure Probability ( Qo) = 0.56
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.34-0.44/(Sqrt(0.2464)/442)
Zo =-4.2354
P-Value: Left Tail -Ha : ( P < -4.23536 ) = 0.00001