please solve it completely 1 A recent political poll of 750

please solve it completely

1. A recent political poll of 750 randomly selected voters found that 680 of them supported the idea of creating a oathway to citizenship for immigrants. Find a 95% confidence interval for the proportion of all voters who support the idea of creating such a pathway to citizenship.

2. An elementry school achievement test is given to third graders in several schools in a particular state. These third graders are assumed to be random sample of all third graders in that state. The sample of n=110 third graders has an average score on the test of 25 and standard deviation of 15. Test the clame that the mean score of all third graders in the state is above 15, and interpret the results in a sentence.

3. suppose you want to test a claim about a proportion, and want the margin of error to be 0.05 with level of significance = .10. Determine the sample size that is required.(There is no estimated value for p.hat)

Solution

1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.906666667          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.010622129          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.020818991          
lower bound = p^ - z(alpha/2) * sp =   0.885847676          
upper bound = p^ + z(alpha/2) * sp =    0.927485657          
              
Thus, the confidence interval is              
              
(   0.885847676   ,   0.927485657   ) [ANSWER]

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