MATH 1F92 Lecture Notes - Lecture 17: Null Hypothesis, Type I And Type Ii Errors, Simple Random Sample

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coraltrout605

18 Mar 2017

School

Brock University

Department

Mathematics and Statistics

Course

MATH 1F92

Professor

Prof.Christian Deangelis

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Document Summary

10. 4- hypothesis tests for a variance or standard deviation. Steps for hypothesis testing a population variance or standard deviation. Step 0: verifying normality: the sample is obtained using simple random sampling or from a randomized experiment, the population is normally distributed. The hypotheses can be structured in one of the following ways: Right-tailed (cid:2777): = (cid:2868) (cid:2778): < (cid:2868) (cid:2777): = (cid:2868) (cid:2777): = (cid:2868) (cid:2778): > (cid:2868) (cid:2778): (cid:2868) (cid:2868) is the assumed value of the population standard deviation. Select a level of significance, , depending on the seriousness of making a type i error. (cid:1872)(cid:2870) and 2 (cid:2870) (cid:1872)(cid:2870) (cid:2869) (cid:2870) (cid:2870) The shaded region is what"s referred to as the critical region. If the test statistic falls within this region, we are able to reject the null hypothesis. This is why drawing the curve and the critical region is helpful. We need to see if the test static lies within the critical region.

Related Questions

The queue manager at a bank believes that their clients spend, on average, less than 15 minutes in the queue. To test his belief the manager commissioned a study, which found out that, from a random sample of 80 customers, the average waiting time was 18 minutes. Assume a population standard deviation of 3 minutes and that the waiting time is approximately normally distributed.
(a) Formulate the null and the alternative hypothesis for this test situation.
(b) Which test statistic (z or t) is appropriate for this test? Give a reason for your answer.
(c) Conduct a hypothesis test for a single mean at 5% significance level. Interpret your results

lemonpig794

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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MATH 1F92 Lecture Notes - Lecture 17: Null Hypothesis, Type I And Type Ii Errors, Simple Random Sample

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