Question

A 2011 Gallup Poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans. Find a 90% confidence interval for the proportion of Americans who would agree with this. Interpret your interval in this context. Explain what “90% confidence” means. Do these data refute a pundit’s claim that 2 / 3 of Americans believe this statement? Explain.

Answer 1

Answer:

Step-by-step explanation:

Let p be the proportion of Americans who believe that high achieving high school students should be recruited to become teachers

Given that p = 0.76 and q = 1-p =0.24

Std error for proportion= $\sqrt{\frac{pq}{n} } \\=0.0135$

For 90% confidence interval we have

0.76±Margin of error

= 0.76±1.645(0.0135)

=0.76±0.0222

thus confidence interval

= (0.7378, 0.7822)

This means we are 90% confidence for randomly selected samples of large size, proportion will fall within this interval

Since proportion lower bound is 73.78% we can say that pundit claim of 2/3 is correct.