STAT2593 Lecture 5: ch 5

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pucecrab517

14 Jun 2016

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Section 5. 3, definitions: statistic: x=sample mean, s2 = sample variance, sampling distribution, is the distribution of the statistic. Section 5. 4, definitions: the distribution of sample mean, let x. 2 n: v x = x = be a random sample from a distribution with mean value and standard n, std. dev x , in addition, with total= t, the sample total: e t o. =n n : proposition: let x and std. dev. N be a random sample from a normal distribution with mean. Then for any n (large or small), bar x is normally distributed with n mean n and stddev. 2: t is normally distributed (see above proposition, st. dev= n 5 0. 35=0. 783. = p 1. 92 z 0. 64 : what is the probability that sample average time. =p z 0. 64 p z 1. 92 =0. 7389 0. 0274=0. 7115 x is at most 2. 0 min x is normally distributed mean x = =1. 5.

Related Questions

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.

bluegiraffe662

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.