A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. The interval that is 95% certain to contain the proportion of all 18-24 year olds who believe that their health is extremely important is ________.
A) between 48% and 54%.
B) between 50% and 52%.
C) between 46% and 56%.
D) between 41% and 61%.

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AlonsoDehner AlonsoDehner · Answer 1 · 2020-01-07T06:26:53+01:00

Answer:

A) between 48% and 54%

Step-by-step explanation:

given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.

Here

Sample size n =1001

sample proportion p = 0.51

Standard error of proportion = [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.51*0.49}{1001} } \\=0.0158[/tex]

Since sample size is sufficiently large we can take Z critical value for confidence interval

Z critical value for 95% = 1.96

Margin of error = ±1.96*std error

= ±0.0310

confidence interval = 0.51 ±0.0310

= (0.48, 0.54)

i.e. A) between 48% and 54%