Question

3.26 Click the icon to view the simulation results. 1 496523 2 483 5 50210 455 Round to one decimal place as needed.)

Answer 1

c)

1)

Level of Significance,   α =    0.05
Sample Size,   n =    1000
      
Sample Proportion ,    p̂ = x/n =    0.496
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4650
Interval Upper Limit , =    p̂ + E =   0.5270

it contains actual proportion of 0.50.

2)

Sample Proportion ,    p̂ = x/n =    0.483
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4520
Interval Upper Limit , =    p̂ + E =   0.5140
it contains actual proportion of 0.50.

3)

Sample Proportion ,    p̂ = x/n =    0.469
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0309
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4381
Interval Upper Limit , =    p̂ + E =   0.4999
it does not contains actual proportion of 0.50.

4)

Sample Proportion ,    p̂ = x/n =    0.464
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0309
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4331
Interval Upper Limit , =    p̂ + E =   0.4949

it does not contains actual proportion of 0.50.

5)

Sample Proportion ,    p̂ = x/n =    0.502
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4710
Interval Upper Limit , =    p̂ + E =   0.5330

it contains actual proportion of 0.50.

6)

Sample Proportion ,    p̂ = x/n =    0.523
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4920
Interval Upper Limit , =    p̂ + E =   0.5540

it contains actual proportion of 0.50.

7)

Sample Proportion ,    p̂ = x/n =    0.515
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4840
Interval Upper Limit , =    p̂ + E =   0.5460

it contains actual proportion of 0.50.

8)

Sample Proportion ,    p̂ = x/n =    0.504
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4730
Interval Upper Limit , =    p̂ + E =   0.5350

it contains actual proportion of 0.50.

9)

Sample Proportion ,    p̂ = x/n =    0.495
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0158
      
margin of error ,    E = Z*SE =    0.0310
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4640
Interval Upper Limit , =    p̂ + E =   0.5260

it contains actual proportion of 0.50.

10)

Sample Proportion ,    p̂ = x/n =    0.455
z -value    "Zα/2 =
"   1.9600
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0157
      
margin of error ,    E = Z*SE =    0.0309
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.4241
Interval Upper Limit , =    p̂ + E =   0.4859

it does not contains actual proportion of 0.50.