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Statistical Sciences 1024A/B Chapter Notes - Chapter 15: Sampling Distribution, Statistical Parameter, Simple Random Sample

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salmonlocust315
20 Apr 2017
School
Western University
Department
Statistical Sciences
Course
Statistical Sciences 1024A/B
Professor
Lori Murray

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Document Summary

A parameter is a number that describes some aspect of the population. A statistic is a number that is computer from the sample and is often used to estimate the unknown parameter. Example: is a population parameter, x is a statistic, x is an estimate of . The population parameter is called the true population mean. 15. 2 statistical estimation and the law of large numbers. The population mean is rarely exactly equal to the population mean. However, if we keep taking large and large samples, the statistic is guaranteed to get closer and closer to the true population parameter. Eventually we will estimate the population mean very accurately. This is called the law of large numbers: as the number of randomly-drawn observations (n) in a sample increases, the mean of the sample gets closer and closer to the population mean. Variability: the sample mean changes sample by sample with each srs of size n.

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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.

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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 

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1. Matt, the manager, wants to estimate the mean wait time for customers to check out in his Mini-Market. He randomly selects customers and determines the mean wait time is minutes. Define the following for this exercise:

a) Is the data collected qualitative or quantitative?

b) Variable (x):

c) Population of Interest:

d) Sample:

e) Parameter of Interest and Statistic: Do you expect the parameter and the statistic to be the same value? Explain.

f) Discuss the use of descriptive and inferential statistics in this exercise.

g) Is the variable, x, discrete or continuous?

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2. Identify the population and sample for the following examples:

The P.E. coach of a middle school interested in the mean height for the graders in the school. He randomly selects graders and measures the height of each.

a) Population:

b) 7thgraders Sample:

c) A community college notices that an increasing number of full-time students are working while attending school. The administration randomly selects 200 students and determines how many hours per week each student works.

1. Matt the Manager wants to estimate the mean wait time for customers to check out in his Mini-Market. He randomly selects 40 customers and determines the mean wait time is 2.7 minutes. Define the following for this exercise:Experimental Unit or Individual: Is the data collected qualitative or quantitative?Variable (x):Population of Interest:Sample:Parameter of Interest:Statistic:Do you expect the parameter and the statistic to be the same value? Explain.Discuss the use of descriptive and inferential statistics in this exercise.Is the variable, x, discrete or continuous?
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2. Identify the populationand samplefor the following examples:a)The P.E. Coach of a middle school interested in the mean height for the 7thgraders in the school. He randomly selects 40 7thgraders and measures the height of each.Population: 7thgraders Sample: 40 7thgraders chosenb)A community college notices that an increasing number of full-time students are working while attending school. The administration randomly selects 200 students and determines how may hours per week each students works.
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