Statistics Task Question Answer 2022

STATISTICS
STUDENT ID:
[Pick the date]

Task - 7.3
Question 1
Sample = 180 bulbs
Number of defective bulbs = 27
Proportion of defective bulbs in factory =?
95% confidence interval =?
Margin of error e =?
Left end point (LEP)=?
Right end point (REP)=?
Conservative margin of error (E)=?
Now,
Proportion of defective bulbs in factory = 27/180 = 0.15
The z value for 95% confidence interval = 1.96
Margin of error = ± z value √ p ( 1−p )
n =±1.96 √ 0.15∗1−0.15
180 =± 0.0522
Left end point (LEP) = p – Margin of error = 0.15 – 0.0522 = 0.0978
Right end point (REP)= p + Margin of error = 0.15 +0.0522=0.2022
Conservative margin of error (E) = C- MOE = (REP-LEP)-MOE = (0.2022-0.0978)-0.0522
=0.0522
Question 2
Sample = 176 people
Number of people found to be infected with HIV = 44
Proportion of infected people =?
99% confidence interval =?
Margin of error e =?
Left end point (LEP)=?
Right end point (REP)=?
Conservative margin of error (E)=?
Now,

Proportion of infected people = 44/176 = 0.25
The z value for 99% confidence interval = 2.58
Margin of error = ± z value √ p ( 1−p )
n =±2.58 √ 0.25∗1−0.25
176 =± 0.0842
Left end point (LEP) = p – Margin of error = 0.25 – 0.0842 = 0.1658
Right end point (REP)= p + Margin of error = 0.25 +0.0842=0.3342
Conservative margin of error (E)= C- MOE = (REP-LEP)-MOE = (0.3342-0.1568)- 0.0842 =
0.0932
Question 3
Sample size =?
Proportion within 0.01 from sample proportion i.e. E = 0.01
95% level of confidence
Proportion = 0.15
n = {(z value)^2 *p(1-p)}/(Margin of error)^2 = (1.96*1.96*0.15*(1-0.15)/(0.01*0.01)
Required sample size n= 4898
Question 4
Sample size =?
Proportion within 0.02 from sample proportion i.e. E = 0.02
99% level of confidence
Proportion = 0.5
n = {(z value)^2 *p(1-p)}/(Margin of error)^2 = (2.58*2.58*0.5*(1-0.5)/(0.02*0.02)
Required sample size n =4147
Task 7.4
Question 1
95% confidence interval for variance of the salary =?
Left end point (LEP)=?
Right end point (REP)=?
Now,