math – math 415 Final Practice Problems

2023-07-09

math 415 Final Practice Problems

math – 这道题目是利用math进行的编程代写任务, 涉及了math等代写方面

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Stat/ math 415 Final Exam Practice Problems

The exam covers Chap 5.1~5.6, Chap 6.4~6.5, 6.8~6.9, Chap 7.1~7.4, 7.6, Chap 8.1~8.4, Chap 9.1~9.3. Final exam will have 5 questions.

You may use a calculator, a hard copy of formula sheet provided on Canvas, Useful Formula.pdf, and three pages of notes (double sided). The distribution tables will be provided. You may NOT use any book or share a calculator with another student without permission of the instructor.

Please carefully review the practice and exam questions for Midterm 1 and 2. Additional practice questions are as follows.

  1. A company wants to determine whether the mean time required to complete a certain task differs among three levels of employee training. The company randomly selected 10 employees from each training level (Beginner, Intermediate, and Advanced), and data are summarized below: Training Level n^ X S^2

Advanced 10 24.2 21. Intermediate 10 27.1 18. Beginner 10 30.2 17. 76

Specify the appropriate null and alternative hypotheses, and use ANOVA to test your hypotheses at the 0.05 significance level. You should complete the ANOVA table below. Source S.S. d.f. M.S. F-ratio Treatment Error Total

  1. A brand of toy is sold in 5 types denoted by A 1 , A 2 , A 3 , A 4 , and A 5. Let pi be the probability that a randomly chosen toy is of type Ai, i = 1, 2, 3, 4, 5. At = 0. 01 , we wish to test H 0 : p 1 = 0.4, p 2 = 0.2, p 3 = 0.2, p 4 = 0.1, p 5 = 0.1 against H 1 : H 0 is not valid, using a random sample of n = 580 toys whose types yielded the frequencies, A 1 : 224, A 2 : 119, A 3 : 130, A 4 : 48, and A 5 : 59.
  2. A random sample of n = 429 people were classified according to sex and according to whether they viewed the newspaper, television or radio as the most credible of all public media. The data are as follows:
Newspaper Television Radio Total
Male 92 108 19
Female 97 81 32
Total

Use the chi-square statistic to test the hypothesis, at the 5% level of significance, that the variables media credibility and sex are independent, and provide the p- value of the test.

  1. To compare the lifetimes of a type of light bulb made in two different factories, A and B, we test independent random samples of 10 bulbs from each factory. The data, in hundreds of hours, are: A : 5.6 4.6 6.8 4.9 6.1 5.3 4.5 5.8 5.4 4. B : 7.2 8.1 5.1 7.3 6.9 7.8 5.9 6.7 6.5 7.
(a) We wish to test H 0 : mA = mB vs. H 1 : mA  mB. Use the sign test to write
down a critical region with level of significance 5%, approximately, and carry
out the test and state your conclusion.

(b) We wish to test H 0 : mA = mB vs. H 1 : mA  mB. Use the Wilcoxon statistic to
write down a critical region with level of significance 5%, approximately, and
carry out the test and state your conclusion.

(c) Use t-test for H 0 : A = B vs. H 1 : A  B with significance level 5%.
  1. Course choosing example: whether the student should take or drop the class if X=0, the first week lectures were boring.