Question 1189975
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In the future, please only post one problem at a time.


I'll do problem 1 to get you started.


n = 400 = sample size
x = 104 = number who have a Samsung phone
phat = x/n = 104/400 = 0.26
The sample proportion phat estimates the population proportion p.


At 90% confidence, the z critical value is roughly z = 1.645 (use a table or calculator to find this value).
We can use the Z distribution because n > 30.


Let's calculate the lower and upper bounds of the confidence interval.


L = lower bound of confidence interval
L = phat - z*sqrt(phat*(1-phat)/n)
L = 0.26 - 1.645*sqrt(0.26*(1-0.26)/400)
L = 0.26 - 0.03607766656811
L = 0.26 - 0.036
L = 0.224


U = upper bound of confidence interval
U = phat + z*sqrt(phat*(1-phat)/n)
U = 0.26 + 1.645*sqrt(0.26*(1-0.26)/400)
U = 0.26 + 0.03607766656811
U = 0.26 + 0.036
U = 0.296


The confidence interval is in the format of (L, U)


Answer: <font color=red>(0.224, 0.296)</font>
We're 90% confident that the population proportion p is somewhere between 0.224 and 0.296
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