Question

2. 55% of respondents who left the house the previous week reported using face masks or face coverings when leaving home. polled from a random sample of 512 people

​​​​​​a. Are conditions satisfied to calculate a confidence interval? Justify your answer.

b.​​​​​Calculate a 99% confidence interval.


​​​​​ c. State what your interval means in the context of the problem.

​​​​​d. Can we say definitively that the majority of Americans are wearing face coverings when leaving the house? Explain.

Answer 1

P( respondents who left the house are wearing a face mask) = 0.55 =

Sample size, n= 512

a) Yes, all the conditions are met to calculate the confidence interval.

The condition of normality is met, as the sample size is large

The samples are drawn randomly

b) 99% Confidence Interval= [ }

= [ ]

= [ ]

= [0.4934, 0.6066]

c) This interval means that we are 90% confident that the proporttion of Americans covering their face while going out is between 0.4934 to 0.6066.

d) NO, The majority of Americans are not wearing the mask because the confidence interval also contaions 0.5 , which is just half the proportion.