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STATS 250 Lecture Notes - Lecture 7: Statistical Parameter, Statistic, Random Variable

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greensalmon921
22 Jan 2016
School
U of M
Department
Statistics
Course
STATS 250
Professor
Brenda Gunderson

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STATS 250 Full Course Notes
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STATS 250 Full Course Notes
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Document Summary

We want to learn about the value of the population mean we take a random sample and use the sample statistic, the sample mean. As it turns out, many normal curve approximations for various statistics are really applications of the. A particular test for measuring various aspects of verbal memory is known as the selective. Scores for various aspects of verbal memory are combined to give an overall score. Let x represent overall score for 20 year old females. Provide a smoothed out sketch of the distribution of the sample mean, include all details that you can. The sampling distribution of a parameter is the distribution of the parameter value if repeated random samples are obtained. This quantity would give us an idea about how far apart a sample mean x and the true population mean are expected to be on average. In practice, the population standard deviation is rarely known, so the sample standard deviation s is used.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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Related Questions

A probability distribution for all possible values of a sample statistic is known as
A.normal distribution
B. uniform distribution random c.sampling sampling distribution
D.sampling distribution

A function of a random variable which describes the probability that random variable is
Select one
A.Probability distribution function
B. Discrete random variable
C. Sampling distribution function
D. Continuous random variable

Consider the normal distribution the vanability is increased and the height of the curve is decreased for the
A. Larger value of standard deviation
B. Smaller value of mean
C. Smaller valie of stabdard deviation
D. Larger value of mean

The sampling destination of the sample mean is a distribution of
A. Sample statistic /estimator
B. individual population values
C. individual sample values
D. Population parameters


The sampling distribution of the mean is distribution of
A. Sample statistic
B. Population parameters
C. individual population values
D. individual sample values

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

(a) gets smaller

(b) becomes larger 

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

(d) becomes negative.

 

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

(a) The sample proportion 

(b) The population proportion 

(c) The population mean

(d) The population mean

 

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.

 

 

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 x̄ 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 x̄= 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.