STATS 250 Lecture Notes - Lecture 8: Sampling Distribution, Bias Of An Estimator, Central Limit Theorem

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amberduck8

26 May 2016

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STATS 250 Full Course Notes

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Stats 250: introduction to statistics - lecture 8: distribution for a sample mean. Sample mean is not equal to the population mean and can change every time we take a new random sample. If all possible random samples of the same size n are taken and x is computed for each, then The average of all of the possible sample mean values is equal to the population mean . The standard deviation is an unbiased estimator of the population mean. The standard deviation of all of the possible sample mean values is equal to the original population standard deviation divided by n. Standard deviation of the sample mean is given by s. d. (x) = / n. If the parent population has a normal distribution, then the distribution of the possible values of x, the sample mean, is normal n( , / n)

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

periwinkleelephant946

Use the following scenario for questions 6 – 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,:µ = 1420 against Hạ: µ > 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.

beigeserval271

Consider the following sample of observations on coating thickness for low-viscosity paint. ("Achieving a Target Value for a Manufacturing Process: A Case Study," J. of Quality Technology, 1992:22-26):

0.83	0.88	0.88	1.04	1.09	1.12	1.29	1.31
1.48	1.49	1.59	1.62	1.65	1.71	1.76	1.83

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

(a) Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

(b) Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

(c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90% and state which estimator you used. [Hint: Express what you are trying to estimate in terms of m and s]

(d) Estimate P(X<1.5), i.e., the proportion of all thickness values less than 1.5 [Hint: if you know the values of and , you could calculate this probability. These values are not available , but they can be estimated.]

(e) What is the estimated standard error of the estimator that you used in part (b)?

skybat612

STATS 250 Lecture Notes - Lecture 8: Sampling Distribution, Bias Of An Estimator, Central Limit Theorem

STATS 250 Full Course Notes

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