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STA450H1 Lecture : ch7.docx

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redwalrus707
26 Apr 2012
School
UTSG
Department
Statistical Sciences
Course
STA450H1
Professor
Mower

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Document Summary

Sampling error: the discrepancy, or amount of error between a sample statistic and its corresponding population parameter. The distribution of sample means: is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population. Sampling distribution: a distribution of statistics obtained by selecting all the possible samples of a specific size from a population. To construct a distribution of sample means: select a sample of size (n), and calculate mean continue to do this until you have selected all the possible samples from the population. The average value of all the sample means is exactly equal to the value of the population mean. Expected value of m: the mean of the distribution of sample means is equal to ( ) and is called the expected value of m.

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Related Questions

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes largerĀ 

(c) stays the same, since the sample size has not been changed

(d) becomes negative.

Ā 

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportionĀ 

(b) The population proportionĀ 

(c) The population mean

(d) The population mean

Ā 

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(c) the resulting margin of error for a confidence interval estimate will tend to be fairly small.

(d) the z distribution must be used to obtain the critical value.

Ā 

Ā 

The queuing time at an airline check-in has a population mean h = 13 minutes and variance o2 = 16 minutes2. Suppose that n = 27 passengers were randomly selected from this population. They were interviewed and reported the queued times. Let xĢ„ defines the sample mean of n observations. Answer the followings:

a) Define your random variable X.

b) Define the sampling distribution of sample mean (indicate a reason and give the name of the distribution, the parameters and sketch it.

c) What is the probability that a sample mean is at most 11 minutes. Please skecth the problem and show all details of your answer.

d) Suppose that for n = 27 passengers, the sample mean is observed as xĢ„= 10 minutes. Based on part c, can we claim that the population mean queuing time is less than 13 minutes.

e) Construct a 95% acceptance region for sample mean of queing time (i.e., u + za x f) Interpret the result obtained in parte and skecth the control chart.