Skip to content
Solved Assignments

Hypothesis Testing and Statistical Evaluation

A homework assignment focused on hypothesis testing and statistical evaluations, helping students understand statistical decision-making.

Preview 10 of 32 pages

See the first 10 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    Page 1 Hypothesis Testing and Statistical Evaluation Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Use the information below to answer Q uestions 1 through 4 . Given a sample size of 36, with sample mean 67 0.3 and sample standard deviatio n 11 4 .9, we perform the following hypothesis test. Null Hypothesis 0 : 700 H  = Alternative Hypothesis : 700 a H   1. What is the test statistic?

  2. Page 2
  3. Page 3
    Read page 3 as text

    Page 2 Answer: 2. At a 10 % significance level (9 0 % confidence level), what is the critical value in this test? Do we reject the null hypothesis?

  4. Page 4
    Read page 4 as text

    Page 3 3. What are the border values between acceptance and rejection of this hypothesis? The border values (also called critical values) between acceptance and rejection are the critical t - values : • Lower border : t=−1.690t = - 1.690t=−1.690 • Upper border : t=+1.690t = +1.690t=+1.690 So, the rejection region is for ttt - values less than - 1.690 or greater than +1.690. The acceptance region is between - 1.690 and +1.690. 4. What is the power of this test i f the assumed tr ue mean were 710 instead of 700?

  5. Page 5
    Read page 5 as text

    Page 4 Next, find the z - score corresponding to the critical value of t=±1.690t = ±1.690t=±1.690 under the null hypothesis: For α=0.10 \ alpha = 0.10α=0.10 and a two - tailed test, the critical value corresponds to t=±1.690t = \ pm1.6 90t=±1.690, which translates to a z - score of 1.690 when the sample size is large enough. Now, calculate the power by finding the probability that the z - score is greater than 1.690 when the true mean is 710. Using a z - table or normal distribution calculator, the probability of a z - score greater than 1.690 is approximately 0.0455 . Thus, the power of this test is 0.9545 (since 1−0.0455=0.95451 - 0.0455 = 0.95451−0.0455=0.9545). Questions 5 t hrough 8 involve roll ing of dice. 5. Given a fair, six - sided die, what is the probability of rolling the die twice and getting a “1” each time? P(A)*P(B) 1/6 * 1/6 = 1/36

  6. Page 6
    Read page 6 as text

    Page 5 6. What is the pro bability of getting a “1” on the second roll when you get a “1” on the first roll? Both events are independent P(A|B) = P(A) 1/6 chance 7. The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1 ” when rolling this loaded die? L oaded dice probability: P(1)+P(2 )+P(2 )+P(3)+P(4 )+P(4)+P(5)+P(6)=1 Getting a 6 when rolling this loaded die = 1/8 = 0.125 8. Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.

  7. Page 7
    Read page 7 as text

    Page 6 Here is the histogram displaying the probability distribution for the loaded die. The heights of the bars represent the probabilities associated with each outcome (1 through 6). As you can see, the outcomes with higher probabilities (such as 2, 3, 5, and 6) have taller bars, while outcomes like 1 and 4 have lower probabilities Use t he data in the table to answer Questions 9 through 1 1 . x 3 1 4 4 5 y 1 - 2 3 5 9 9. Determine SS xx , SS xy , and SS y y .

  8. Page 8
    Read page 8 as text

    Page 7

  9. Page 9
    Read page 9 as text

    Page 8 10. Find the equation of the regression line. What is the predicted value when 4? x = 11. Is the correlation significant at 1 % significance level ( 99 % confidence level ) ? Why or why not?

  10. Page 10
    Read page 10 as text

    Page 9 Use the data below to answer Q uestions 1 2 through 1 4 . A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follow s : Football Basketball Soccer Maryland 60 70 20 Duke 10 75 15 UCLA 35 65 25 Supposed a student is randomly selected from the group mentioned above. 12. What is the probability that the student is from UCLA or chooses football?

22 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Statistics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.