Question

Only 4 in 10 registered voters believe that President Donald Trump is fit for office. While 86 percent of self-identified Republicans said Trump is fit to serve, an overwhelming 93 percent of Democrats said the OPPOSITE. The survey of 1577 voters was conducted. It has a margin of error of plus or minus 3%.

b. Construct the 95% CI estimate of the population proportion of registered voters who believe the President is fit for office.

c. Explain why NEITHER the 86 percent of Republicans NOR 7 percent of Democrats who believe Donald Trump is fit for office is a good estimate of the population proportion of ALL registered voters who believe the President is fit for office.

e. Compute the probability that i) 5 of 10 randomly selected Republicans believe that the President is fit for office.

ii) the probability that 5 randomly selected Democrats believe that the President is fit for office. Use the probability estimate provided.

Answer 1

b)

margin of error , E = 0.03
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.400   -   0.03 =   0.37
Interval Upper Limit = p̂ + E =   0.400   +   0.03   =   0.43
                  
95%   confidence interval is (   0.37 < p <    0.43   )

c)

As you can see neither democrats (0.07) or Republicans (0.86) are in above confidence interval.It means these are good estimater of population proportion.

e. Compute the probability that i) 5 of 10 randomly selected Republicans believe that the President is fit for office

p = 0.86

n =10

P ( X =    5   ) = C(10,5) * 0.86^5 * (1-0.86)^5 =            0.006376

ii) the probability that 5 randomly selected Democrats believe that the President is fit for office. Use the probability estimate provided.

p = 0.07

n =10

P ( X = 5   ) = C(10,5) * 0.07^5 * (1-0.07)^5 =            0.0002946

Please revert in case of any doubt.

Please upvote. Thanks in advance