Statistik Industri  October 18, 2008Posted by desrinda in Statistik Industri.
A point estimate is a single number. For the population mean (and population standard
deviation), a point estimate is the sample mean (and sample standard deviation).
A confidence interval provides additional information about variability.
1. What is meant by “the sampling distribution of the mean”?
2. What does the central limit theorem say? Why is it useful?
3. How is the population mean of the sample average related to the population mean of individual observations?
4. What is the standard error of the mean, and what do we use it for?
5. What happens to the sampling distribution of the mean if (i) the sample size is increased, (ii) the population standard deviation is decreased?
6. Using 4 your Standard Normal table, verify that :
– 90 % of the area under the standard normal curve (i.e N(0,1) corresponds to Z= ± 1.65;
– 95 % of the area under the standard normal curve corresponds to Z = ± 1.96
– 99 % of the area under the standard normal curve corresponds to Z = ± 2.58
7. Students in MA238 spend on average 3.75 hours a week studying ( with a population standard deviation σ = 5.17 )
i. Given this fact, describe the sampling distribution of the mean if all possible random sample size 50 were chosen.
ii. What can you say about the mean off all the possible sample means?
iii. If 250 such samples were chosen at random and for each you calculated a 95% C.I for the mean, how many such intervals would you expect to contain the true mean?
iv. If instead you calculated a 99% C.I. for the mean, how many intervals would you now expect to capture the true mean.
v. Would you expect the 99% C.I. for the mean to be narrower or wider than the corresponding 95 % C.I. for the mean. Justify your answer!
8. The director of quality at a light bulbs factory needs to estimate the average life of a large shipment of light bulbs. A random sample of 64 light bulbs indicated a sample average life 350 hours with sample standard deviation of 100 hours.
a) Construct and interpret a 95% confidence interval estimate of the true average life of light bulbs in this shipment.
b) Do you think the manufacturer has the right to state that the light bulbs last an average 400 hours? Explain.
c) Does the population have to be normally distributed here for the interval to be valid? Explain.
d) Explain why an observed of 320 hours is not unusual, even thought it outside it is outside the 95% confidence interval you have calculated.
e) Suppose that the sample average had been 300 hours. What would be your answer to a) ?
9. A newspaper headline describing a poll of registered voters taken two weeks before a recent election reads “Aitchison lead with 525. The accompanying article describing the poll state that the margin of the error was 2% with 95% confidence.
a) Explain in plain language to someone who knows no statistics what “95% confidence “ means?
b) The poll shows Aitchison leading. But the newspaper article said that the election was too close to call, Explain why?
10. A student reads that a 95% confidence interval for the mean maths score leaving sert students in 45 to 47 %. Asked to explain the meaning of this interval, the student says, 95% of leaving cert students have math score between 451 and 47%. Is the student right? Justify your answer.