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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.

a) Find a 90% confidence interval for the proportion of Americans who would agree with this.
b) Interpret your interval in this context.
c) Explain what “90% confidence” means.
d) Do these data refute a pundit’s claim that 2>3 of Americans believe this statement? Explain.

Respuesta :

Answer:

Step-by-step explanation:

Given that Gallup poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers

Sample size n=1002

a) 90% Z critical=1.645

Std error = [tex]\sqrt{\frac{pq}{n} }[/tex]

=0.0135

Margin of error = ±2.22%

Confidence interval = (73.78%, 78.22%)

b) We can be 90% sure that for sample sizes large and samples drawn at random the proportion of high achieving school students becoming teachers lie between these two values

c)  We are 90% confidence that for large random samples, the desired proportion will lie within these values.

d) Yes because lower limit 73.78% itself is higher than 2/3

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