Question 974214
(a)


Given:
x = 856
n = 1007



p-hat = x/n
p-hat = 856/1007
p-hat = 0.85004965243297


The point estimate is approximately <font color="red">0.85004965243297</font>


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(b)


Given:
x = 856
n = 1007
p = 0.75
phat = 0.85004965243297 (found in part a)
alpha = 0.01



Hypothesis:
H0: p = 0.75
H1: p > 0.75 (claim)


Standard Error:
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.75*(1-0.75)/1007)
SE = 0.0136453883651


Test Statisic:
z = (phat - p)/SE
z = (0.85004965243297 - 0.75)/0.0136453883651
z = 7.3321220148531


p-value
normalcdf(7.3321220148531, 99999) = 1.14 * 10^(-13)
The p-value is so very small that it's effectively 0.
No matter what the significance level is, we have statistically significant evidence to reject H0.


Decision: Reject the null hypothesis


Conclusion: There is enough significant evidence to conclude that the population proportion who are familiar with twitter is over 75%


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