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A poll of 2,015 randomly selected adults showed that 97​% of them own cell phones. The technology display below results from a test of the claim that 94​% of adults own cell phones. Use the normal distribution as an approximation to the binomial​ distribution, and assume a 0.05 significance level to complete parts​ (a) through​ (e).


Hypothesis
p = 0.94
p != 0.94

alpha = 0.05

use of z-test to test the Hypothesis. 

n = 2015
p = 0.94

p_hat = 0.97

z = (p_hat - p)/sqrt((p*(1-p))/n)


z = 5.67

pnorm(q = z, lower.tail = FALSE)

Reject the Null hypothesis, there is sufficient evidence that to conclude that the proportion is different. 

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