Suppose a random sample of 70 patients from the QEII Hospital, contained 45 fema

Question

Suppose a random sample of 70 patients from the QEII Hospital, contained 45 females and 25 males. a.) Compute a point estimate of the proportion of females among hospital patients. (Give decimal answer to 2 places past decimal, without a leading zero). b.) Determine a 90% confidence interval for the proportion of females at that hospital. (Give decimal answer to 2 places past decimal, without a leading zero.) CI Lower Bound: CI Upper Bound: c.) Determine a 95% confidence interval for the proportion of males at that hospital. (Give decimal answer to 2 places past decimal, without a leading zero). CI Lower Bound: CI Upper Bound:

Explanation / Answer

a.
No. of success(x)=45
Sample Size(n)=70
Sample proportion = x/n =0.643
b.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Confidence Interval = [ 0.643 ±Z a/2 ( Sqrt ( 0.643*0.357) /70)]
= [ 0.643 - 1.645* Sqrt(0.003) , 0.643 + 1.65* Sqrt(0.003) ]
= [ 0.549,0.737]
c.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=45
Sample Size(n)=70
Sample proportion = x/n =0.643
Confidence Interval = [ 0.643 ±Z a/2 ( Sqrt ( 0.643*0.357) /70)]
= [ 0.643 - 1.96* Sqrt(0.003) , 0.643 + 1.96* Sqrt(0.003) ]
= [ 0.531,0.755]

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