# statistics assignment

Week 5

It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA, Coffee Pot Attendant.

It is a very important office sponsored by the Holy See.

I have taken this job very seriously, because I believe that I am the key to increased productivity at the Undergraduate School. Why, by mid-morning, many of my colleagues act as if they were

It is imperative that I restore productivity via a secret naturally-occurring molecule, caffeine……..

In order to see if my secret molecule works, I have observed the time, in hours, a random selection of ten of my colleagues who could stay awake at the extremely long-winded Dean’s meeting as soon as it started. Oh, yes, one fell asleep even before the meeting started!

1.9 .8 1.1 .1 -.1

4.4 5.5 1.6 4.6 3.4

Now, I have to complete a report to the Provost’s Office on the effectiveness of my secret molecule so that UMUC can file for a patent at the United Provinces Patent and Trademark Office as soon as possible. Oh, yes, I am waiting for a handsome reward from the Provost…..

But I need the following information:

•What is a 95% confidence interval for the time my colleagues can stay awake on average for all of my colleagues?

•Was my secret molecule effective in increasing their attention span, I mean, staying awake? And, please explain…..

Week 6

In the North American court system, a defendant is assumed innocent until proven guilty. In an ideal world, we would expect that the truly innocent will always go free, whereas the truly guilty ones will always be convicted. Now, let us tackle the following questions?

1.In the context of the Type I error and Type II error, can you relate a court trial scenario in terms of these two errors?

2.What would be your ideal situation if you are the defendant?

3.What would be your ideal situation if you are the prosecuting attorney?

4.Lastly, what do you think of the scenario of an ideal world where we expect that no innocent will be found guilty and all guilty will be convicted in the context of Type I error and Type II error?

Week 7

My younger brother had a run in earlier with Médecins Sans Frontières. He narrowly escaped from an adverse verdict by the court…….. What he wants is that he be left alone to run his small café……

He asked my oldest brother if he can conduct a survey for him about justice in the Kangaroo Court. Oooops, I mean the Canadian Court……

An initial survey was performed right after Médecins Sans Frontières accused my brother of wrong doing. Of 1852 customers, 53 were against the aggressive tactics of Médecins Sans Frontières. After my brother was cleared by the court, a follow-up survey was performed. Of 4699 customers, 1751 said they did not agree with the aggressive tactics of Médecins Sans Frontières

At the 1% significance level, do the data suggest that a higher percentage of customers were against Médecins Sans Frontières after the court case?

He is now hiding in the kitchen………… Can we restore his faith in his customers? Oooops, no Gendarmerie Royale du Canada.

Week 6 Homework

- You choose an alpha level of .01 and then analyze your data.
- What is the probability that you will make a Type I error given that the null hypothesis is true?
- What is the probability that you will make a Type I error given that the null hypothesis is false?

- Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subject’s get- ting better each trial? Test the linear effect of trial for the data.

A | b | c |

4 | 6 | 7 |

3 | 7 | 8 |

2 | 8 | 5 |

1 | 4 | 7 |

4 | 6 | 9 |

2 | 4 | 2 |

- Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
- Compute a one-sample t-test on this column (with the L values for each subject) you created.

- You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The ﬁrst group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100.
- What is the calculated t value? Are the mean test scores of these two groups signiﬁcantly different at the .05 level?
- What would the t value be if there were only 6 participants in each group? Would the scores be signiﬁcant at the .05 level?

- Rank order the following in terms of power.

Population 1 mean | n | Population 2 mean | Standard deviation | |

A | 29 | 20 | 43 | 12 |

B | 34 | 15 | 40 | 6 |

C | 105 | 24 | 50 | 27 |

D | 107 | 2 | 120 | 10 |

- Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:
- Ho: x ¯ = 4.5,Ha : x ¯ > 4.5
- Ho:μ≥ 4.5,Ha:μ< 4.5
- Ho:μ= 4.75,Ha:μ> 4.75
- Ho:μ= 4.5,Ha:μ> 4.5

- Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:
- to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
- to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
- to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
- to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

- An article in the News stated that students in the state university system take 4.5years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?
- H0: _______
- Ha: _______
- In words, CLEARLY state what your random variable X ¯ or P′ represents.
- State the distribution to use for the test. e. What is the test statistic?
- What is thep-value? In one or two complete sentences, explain what the p-value means for this problem.
- Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
- Alpha: _______
- Decision: _______

- Reason for decision: _______ i

- Conclusion: _______
- Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

- At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Relaxed time (seconds) | Jumping time (seconds) |

26 | 21 |

47 | 40 |

30 | 28 |

22 | 21 |

23 | 25 |

45 | 43 |

37 | 35 |

29 | 32 |

- H0: _______
- Ha: _______
- In words, CLEARLY state what your random variable X ¯ or P′ represents.
- State the distribution to use for the test. e. What is the test statistic?
- What is thep-value? In one or two complete sentences, explain what the p-value means for this problem.
- Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Indicate the correct decision (“reject” or “do not reject” the nullhypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
- Alpha: _______
- Decision: _______

- Reason for decision: _______ i

- Conclusion: _______
- Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

- A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45pounds with a standard deviation of 14 pounds.
- H0: _______
- Ha: _______
- In words, CLEARLY state what your random variable X ¯ or P′ represents.
- State the distribution to use for the test. e. What is the test statistic?
- What is thep-value? In one or two complete sentences, explain what the p-value means for this problem.
- Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Indicate the correct decision (“reject” or “do not reject” the nullhypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
- Alpha: _______
- Decision: _______

- Reason for decision: _______ i

- Conclusion: _______
- Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

- A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takesfournewstudents.Sherecordstheir18-holescoresbeforelearningthetechniqueandthenafterhavingtakenherclass. She conducts a hypothesis test. The data are as follows.

Player 1 | Player 2 | Player 3 | Player 4 | |

Mean score before class | 83 | 78 | 93 | 87 |

Mean score after class | 80 | 80 | 86 | 86 |

The correct decision is:

- Do not reject the H0.

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