STA301 Statistics and Probability Assignment 4 Solution Fall 2012

Question 1: (Marks: 2+5=7)
a. In a finite population with and , find the mean and variance for the sampling distribution of sample mean for n = 25.

b. The mean and standard deviation of the maximum loads supported by 50 cables are 13 tons and 0.80 tons respectively. Find the 99% confidence interval for the mean of the maximum loads of all cables produced by the company. Also interpret the findings.
Question 2: (Marks: 5+3=8)
If is normally distributed with and .
Find the
A sample of people at the university cafeteria on meatless day showed 20% of them preferred vegetable dishes. How large a sample is needed if we want to be 95% confident that our estimate of population proportion is within 0.03?

Solution:

If the say 95% confidence interval has been determined (statistically perhaps by least squares fit) there is a 95% confidence that the real value is within the calculated interval. The center of the interval is the most likely value (for the amount of data processed) and is the top of a bell curve (unless the data are skewed). Usually the more data that are processed the smaller the 95% confidence interval will be(although ‘flyers’ due to obvious error must be eliminated). If you are processing the height of human beings and only one is listed as 23 feet tall, likely there has been a recording error producing a flyer. If you process the heights of 50 people, the 95% confidence interval in the value of average human height will be less refined than if you process the height of 1,000 people or 10,000