Question

Question 4: Confidence Intervals: Each question is worth 7.5 marks: Total A. Suppose we know the population standard deviation is 0.03. We have a sample size of 121. We also have a sample proportion of 0.65 and a confidence interval of 90%. Find the interval for the population proportion with 90% confidence level? ________________________________ B. Suppose we know the population standard deviation is 4. We have a sample size of 144. We also have a sample mean of 55 and a confidence interval of 82%. Find the interval for the population mean with 82% confidence level?

Answer 1

If population standard deviations are known then we will use z statistic to construct confiedance interval

Sample proportion (X_)=0.65

Population standard deviation=0.03

Sample size=121

z-statistic for 90% confiedance level=1.64

Confiedance interval for population proportion(¶_) is

(X_-(population standard deviation/(square root of sample size))*z(at 90% confiedance),X_+(population standard deviation/(square root sample size)*z(at 90% confiedance)

(X_-(0.03/sqrt(121)*1.64,X_+(0.03/sqrt(144)*1.64)

(X_-0.0492/11,X_+0.0492/12)

(0.65-(0.0492/11),0.65+(0.0492/11))

Ans 2)

Using the same logic we can calculate confiedance interval for second part of question as follows

(X_-(4/sqrt(144))*1.34,X_+(4/sqrt(144))*1.34)

(55-0.446,55+0.446)