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STAT 1000Q Lecture Notes - Lecture 14: Statistical Parameter, Standard Deviation, Sampling Distribution

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Verified Note
purplejackal312
8 Mar 2019
School
UConn
Department
Statistics
Course
STAT 1000Q
Professor
Robert Apruzese

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STAT 1000Q Lecture Notes - Lecture 13: Electric Light, Normal Distribution, Wear

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STAT 1000Q Lecture Notes - Lecture 14: Statistical Parameter, Standard Deviation, Sampling Distribution

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STAT 1000Q Lecture 15: Week 8 Cornell-style Notes [TYPED]

Document Summary

Stat 1000q lecture 14 - sampling distribution of sample mean and clt population parameter- a xed numerical feature of a population, usually unknown. Examples: population mean , population standard deviation , b(n, p): parameters n, p, u(a, b): parameters a, b sample statistic- a numerical value computed from sample data. Examples: sample mean x , sample standard deviation s sampling distribution of x - a probability distribution based on the collection of all the x computed from all possible samples of size n from population n. Suppose: we have a large population of size n. From n, we repeatedly select random samples of a xed size n n is less than n because it is within n. From each sample, we compute the sample mean x . These samples of size 100 are all random. Since x is random if the samples are random, the x here are all random.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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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.

Use the following scenario for questions 6 ā€“ 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:Āµ = 1420 against Hįŗ”: Āµ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.