Question

In a nationwide poll the proportion of respondents who thought that it should be illegal to use a handheld cellphone while driving a car was p̂ =0.7p^=0.7. The poll's sample size was 673.

1. What is the standard error of the sample proportion p̂ p^? [answer to 4 decimal places]

2. Suppose pp denotes the population proportion of respondents who think that it should be illegal to use a handheld cellphone while driving a car. Which of the following options gives the formula for conservative interval estimate for pp?
a. 0.7∓0.0177673‾‾‾‾√0.7∓0.0177673
b. 0.0177∓1673‾‾‾‾√0.0177∓1673
c. 0.0177∓0.7673‾‾‾‾√0.0177∓0.7673
d. 0.7∓1673‾‾‾‾√0.7∓1673

3. Which of the following formulas gives the 90% confidence interval for pp?
a. 0.7∓2.576×0.01770.7∓2.576×0.0177
b. 0.7∓1.645×0.01770.7∓1.645×0.0177
c. 0.7∓1.96×0.01770.7∓1.96×0.0177
d. 0.7∓2.326×0.01770.7∓2.326×0.0177

4. What is the margin of error of the 90% confidence interval of pp [answer to 4 decimal places]

Answer 1

1)

Sample Size,   n =    673          
                  
Sample Proportion ,    p̂ = 0.700          
                  
Standard Error ,    SE = √( p(1-p)/n ) =    0.0192          

2)

formula for conservative interval estimate for p= p^ ± 1/√n

so, answer is  d. 0.7∓1/√673

3)

Level of Significance,   α =    0.10
z -value =   Zα/2 =    1.645
90%   Confidence Interval is (p̂ ± Z*std error) = (0.70 ±1.645*0.0177)

answer: option b

4)

margin of error , E = Z*SE =    1.645   *   0.0177   =   0.0291