Question 974214: The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is.
a.What is the point estimate for the number of adults who know what Twitter is?
b.Use a 0.01 level of significance to test the claim that more than 75% of adults know what Twitter is.
State the null and alternative hypotheses:
Calculate the test statistic:
Fine the p-value:
Decision:
Conclusion:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! (a)
Given:
x = 856
n = 1007
p-hat = x/n
p-hat = 856/1007
p-hat = 0.85004965243297
The point estimate is approximately 0.85004965243297
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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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