STAT 100 Lecture Notes - Lecture 16: Normal Distribution, Standard Deviation, Sampling Distribution

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browntermite554

10 May 2017

School

University of Maryland

Department

Statistics and Probability

Course

STAT 100

Professor

Cremins

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Document Summary

Because the values of the sample proportion varies from sample to sample, it is a random variable. So, we have the same questions for the sample proportion as we had for the sample mean: What is the mean of the sample proportion? p. How do we nd the critical value for our con dence interval? statistic +/- (critical value) x (standard deviation of statistic) If the normal condition is met, we can use a normal curve. To nd a level c con dence interval, we need to catch the central area c under the standard normal curve. For example, to nd a 95% con dence interval, we use a critical value of 2 based on the. Using a standard normal table or a calculator, we can get a more accurate critical value. Note, the critical value z* is actually 1. 96 for a 95% con dence level.

Related Questions

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

(a) gets smaller

(b) becomes larger

(d) becomes negative.

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

(a) The sample proportion

(b) The population proportion

(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.

(d) the z distribution must be used to obtain the critical value.

periwinkleyellowjacket100

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.

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STAT 100 Lecture Notes - Lecture 16: Normal Distribution, Standard Deviation, Sampling Distribution

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