Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,

n=988 and x=505 who said​ "yes." Use a 99% confidence level.

a) Find the best point estimate of the population proportion p.

​b) Identify the value of the margin of error E.

​c) Construct the confidence interval.

< p <

​d) Write a statement that correctly interprets the confidence interval.

Answer 1

Here we have given that

n=Total number of person=988

x: number of person who said "Yes"= 505

(A)

we know that the best point estimate of the population proportion P is the sample proportion

Now, we estimate the proportion p as

=sample proportion =

(B)

we want to find the 95% confidence interval for population proportion P

Formula for CI is as follows,

Where,

E=Margin of error =

Now we find Z-critical

C=confidence level=0.95

=level of significance= 1-c=1-0.95=0.05

==1.96 Using excel = NORMSINV(probability = 0.05/2)

Now,

E=Margin of error =

=

= 0.031

The Margin of error value is 0.031

(C)

we get the 95% confidence interval is as follows,

Lower limit= 0.48

Upper limit=0.54

(D)

Conclusion:

Here we can say that we are 95 % confident that the population proportion is lies within that interval.