In a poll 412 of 1010 randomly selected adults aged 18 of old stated that they b

Question

In a poll 412 of 1010 randomly selected adults aged 18 of old stated that they believe there is too little spending on national de information to complete parts (a) through (e) below. Obtain a point estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense. Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence interval about p satisfied ? Yes the requirements for constructing a confidence interval are satisfied No the requirement that the sample size be a simple random sample is not satisfied. No. the requirement that the sample sire is no more than 5% of the population is not satisfied No. the requirement that np^^(1 - p^) is greater than 10 is not satisfied Construct a 90% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national the 90% confidence interval is

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n = 412/1030 =   0.4   [ANSWER]

****************************

b)      

As we can see, all options b to d are false, as those requirements are satisfied, so

OPTION A: Yes, the requirements are satisfied. [ANSWER]

***************************

c)
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.015264656          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.025108124          
lower bound = p^ - z(alpha/2) * sp =   0.374891876          
upper bound = p^ + z(alpha/2) * sp =    0.425108124          
              
Thus, the confidence interval is              
              
(   0.374891876   ,   0.425108124   ) [ANSWER]

********************************

d)

As the whole interval is less than 0.45, it is very very unlikely. [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.