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Hypothesis Testing and Statistical Evaluation - Document preview page 1

Hypothesis Testing and Statistical Evaluation - Page 1

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Hypothesis Testing and Statistical Evaluation

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

Lucas Allen
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12 months ago
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Hypothesis Testing and Statistical Evaluation - Page 1 preview imagePage1Hypothesis Testing and Statistical EvaluationMake sure your answers are as complete as possible.Show all of your workand reasoning.In particular, when there are calculations involved, you mustshow how you come up with your answers with criticalwork and/or necessarytables.Use the information below to answer Questions1 through 4.Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, weperform the following hypothesis test.Null Hypothesis0:700H=Alternative Hypothesis:700aH1.What is the test statistic?
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Hypothesis Testing and Statistical Evaluation - Page 3 preview imagePage2Answer:2.At a 10% significance level (90% confidence level), what is the critical value in this test?Do we reject the null hypothesis?
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Hypothesis Testing and Statistical Evaluation - Page 4 preview imagePage33.What are the border values between acceptance and rejection of this hypothesis?Theborder values(also called critical values) between acceptance and rejection are thecriticalt-values:•Lower border:t=−1.690t =-1.690t=−1.690•Upper border: t=+1.690t = +1.690t=+1.690So, the rejection region is for ttt-values less than-1.690 or greater than +1.690. The acceptanceregion is between-1.690 and +1.690.4.What is the power of this test if the assumed true mean were 710instead of 700?
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Hypothesis Testing and Statistical Evaluation - Page 5 preview imagePage4Next, find the z-score corresponding to the critical value of t=±1.690t = ±1.690t=±1.690 underthe null hypothesis:For α=0.10\alpha = 0.10α=0.10 and a two-tailed test, thecritical valuecorresponds to t=±1.690t=\pm1.690t=±1.690, which translates to a z-score of 1.690 when the sample size is largeenough.Now, calculate thepowerby finding the probability that the z-score is greater than 1.690 whenthe true mean is 710.Using a z-table or normal distribution calculator, the probability of a z-score greater than 1.690 isapproximately0.0455.Thus, thepowerof this test is0.9545(since1−0.0455=0.95451-0.0455 =0.95451−0.0455=0.9545).Questions 5through8involverollingof 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
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Hypothesis Testing and Statistical Evaluation - Page 6 preview imagePage56.What is the probability of getting a “1” on the second roll when you get a “1” on the firstroll?Both events are independent P(A|B) = P(A)1/6 chance7.The House managed to load the die in such a way that the faces “2” and “4” show uptwice as frequently as all other faces. Meanwhile, all the other faces still show up withequal frequency. What isthe probability of getting a “1” when rolling this loaded die?Loaded dice probability: P(1)+P(2)+P(2)+P(3)+P(4)+P(4)+P(5)+P(6)=1Getting a 6 when rolling this loaded die = 1/8 = 0.1258.Write the probability distribution for this loaded die, showing each outcome and itsprobability. Also plot a histogram to show the probability distribution.
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Hypothesis Testing and Statistical Evaluation - Page 7 preview imagePage6Here is the histogram displaying the probability distribution for the loaded die. The heightsof the bars represent the probabilities associated with each outcome (1 through 6). As youcan see, the outcomes with higher probabilities (such as 2, 3, 5, and 6) have taller bars,while outcomes like 1 and 4 have lower probabilitiesUse the data inthe table to answer Questions 9through11.x31445y1-23599.Determine SSxx, SSxy, and SSyy.
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Hypothesis Testing and Statistical Evaluation - Page 9 preview imagePage810.Find the equation of the regression line. What is the predicted value when4?x=11.Is the correlation significant at1% significance level (99% confidence level)? Why orwhy not?
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Hypothesis Testing and Statistical Evaluation - Page 10 preview imagePage9Use the data below to answer Questions12through 14.A group of students from three universities were asked to pick their favorite college sportto attend of their choice: The results, in number of students, are listed as follows:FootballBasketballSoccerMaryland607020Duke107515UCLA356525Supposeda student is randomly selected from the group mentioned above.12.What is the probability that the student is from UCLA or chooses football?
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Statistics

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