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DerKrebs [107]
3 years ago
15

YThe Pew Research Center conducted a survey of 1007 adults and found that 85% of them know what Twitter is. Find a 90% confidenc

e interval for the proportion of all adults who know what Twitter is. Also find the margin of error. Round all of your answers to four decimal places.
Mathematics
1 answer:
goblinko [34]3 years ago
6 0

Answer:

The 90% confidence interval is   0.8315 <  p < 0.8685

Step-by-step explanation:

From the question we are told that

   The sample size is n =  1007  

    The sample proportion is  \^ p =  0.85

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.10

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.645

Generally the margin of error is mathematically represented as  

      E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p(1- \^ p)}{n}}

=>   E =1.645 * \sqrt{\frac{0.85 (1- 0.85 )}{1007}}

=>   E = 0.0185    

Generally 90% confidence interval is mathematically represented as  

      \^ p -E <  p <  \^ p +E

=>  0.85 -0.0185 <  p < 0.85 + 0.0185

=>  0.8315 <  p < 0.8685

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<h3>How to solve the inequality?</h3>

Here we have the inequality:

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brainly.com/question/24372553

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Step-by-step explanation:

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Step-by-step explanation:

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