Please show ALL work 1 A political science student at a larg

Please show ALL work.

1.) A political science student at a large university wants to determine the percent of students that are registered voters. He surveys 500 students and finds that 300 are registered voters. Compute a 90% confidence interval for the true percent of students that are registered voters.

2.) A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 30 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a 90% confidence interval for the mean time to process rebates.

3.) A researcher wants to determine the proportion of U. S. households that use email.An earlier study found 42 % of households used email.How many households must be sampled in order to be 94% confident that the margin of error is within 3%?

4.) A law school wants to know how successful its graduates are at passing the bar exam on the first try. Two hundred graduates are randomly selected and asked whether they passed the bar exam the first time they took it. Of the 200 graduates, 130 said they passed the exam on the first try. Set a 98% confidence interval for the proportion of law student graduates at this university who passed the bar exam.

Solution

1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.6          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.021908902          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.563963063          
upper bound = p^ + z(alpha/2) * sp =    0.636036937          
              
Thus, the confidence interval is              
              
(56.3963063% , 63.6036937%) [ANSWER]

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