Question

Question 3: Confidence Intervals: Each question is worth 7.5 marks - Total A. A sample of 121 customers revealed that 65% of them would like to use on-line shopping facilities. Find a 90% confidence interval for the population proportion of customers who would like to use on-line shopping facilities. Page 3 of 7 B. Suppose we know that the population standard deviation is 3. We have a sample size of 64. We also have a sample mean of 35. Estimate the population mean with 95% confidence.

Answer 1

Solution(3)
No. of sample = 121
p = 0.65
1-p = 0.35
alpha = 0.1
Zalpha/2 = 1.645
90% confidence interval can be calculated as
p +/- Zalpha/2*sqrt(p*(1-p)/n
0.65+/-1.645*sqrt(0.65*0.35/121)
0.65+/-1.645*0.0433
0.65 +/- 0.0713
So 90% confidence interval is
0.5787 to 0.7213

Solution(b)

Sample Size = 64
Sample Mean = 35
Population standard deviation = 3
95% confidence interval is
mean +/- Zalpha/2*SD/sqrt(n)
35+/- 1.96*3/sqrt(64)
35 +/- 0.735
so 95% confidence interval is
34.265 to 35.735