Qmeth 201- intro to statistical method homework

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Total

Question 1 (12 points)

Settle Brewing Company sells 32 oz bottles of beer. The machine which fills the bottles is not very consistent. Though it fills the bottles on average with 32 oz. of beer, there is variation, and the standard deviation for the amount of beer filled in the bottles is 0.4 oz. Suppose that the manager of the plant randomly samples one bottle from each day’s production. Assume that the amount of beer filled in a bottle can be described by a normal distribution. Answer the following questions (treat each question independent of other questions). a. Estimate the probability that today’s sampled bottle is overfilled. b. Estimate the probability that of the seven bottles sampled last week, five or more were overfilled. c. Estimate the probability that a randomly sampled bottle contains 31.5 to 33 oz. of beer. d. Estimate the probability that yesterday’s sampled bottle contained 32.4 oz of beer.

Question 2 (10 points) (Write down your choices and the reasoning on white or ruled sheets. Do not circle the responses here)

A large data set has the following summary statistics:

mean = 40 minimum = 20 standard deviation = 10 maximum = 60 Suppose that two new observations, 0 and 80 are added to the data set.

a. What happens to the median?

Increases Decreases Remains the same Will increase by 10 Cannot be determined

b. What happens to the mean? Increases Decreases Remains the same Will increase by 10 Cannot be determined

c. What happens to the standard deviation?

Increases Decreases Remains the same Will increase by 10 Cannot be determined

d. What happens to the range?

Increases Decreases Remains the same Will increase by 10 Cannot be determined

e. What happens to the mode?

Increases Decreases Remains the same Will increase by 10 Cannot be determined

Question 3 (15 points)

You are exploring the music in your iTunes library. The total play counts over the past year for the 26 songs on your “smart playlist” are shown below.

128 56 54 91 190 23 160 298 445 50 578 464 37 677 17 74 70 868 108 71 466 23 84 38 26 814

a. Determine the appropriate number of classes, and make a frequency distribution of the counts. b. Describe and comment on the distribution. c. It is often claimed that “a small fraction of the items account for largest proportion of use”. This is also known as Pareto’s Law. Is this

claim validated in this data set? d. Classify the above data set – is it observational or experimental? is it cross sectional or time series, is it quantitative or qualitative, is it

primary or secondary data, what is the level of measurement for the data set?

Question 4 (10 points)

Consider the data provided to you as part of question 56 on page 81 in the text (chapter 3). Answer the following:

a. Answer the questions posed in the text. b. Determine the median for the data set. Explain how you arrived at your answer. c. Determine the mode. Explain how you arrived at your answer. d. Determine the interquartile range. Show details of how you arrived at your answer. e. Identify all outliers, if there are any. Show details of how you arrived at your answer.

Question 5 (10 points)

A file containing the ages of all US President (“Presidents.xlsx”) is provided to you on Canvas under the module, “Midterm Examination”. Using Excel or otherwise, determine the following:

a. All measures of central tendency discussed in the class. b. Determine the standard deviation. c. Develop a box plot. Clearly indicate the minimum value, all quartile values and maximum value. d. Are there any outliers? If so, who are they? e. Is the distribution symmetric or skewed? If it is skewed, is it positively skewed or negatively skewed? Explain why you came to that

conclusion.

Question 6 (12 points)

You are participating in a game show with five doors. There is just one prize behind one of those five doors. After you select a door, the game host opens three of the other four remaining doors which do not have the prize behind them. At that point, you are given an opportunity to change your mind, and switch to the other unopened door. Should you switch? Explain your analysis using probability trees.

Question 7 (12 points)

A repair shop has two technicians with different levels of training. The technician with advanced training is able to fix problems 92% of the time, while the other has success rate of 80%. Assume you have a 20% chance of obtaining the mechanic with advanced training.

a. Draw the contingency table for this problem. b. Find the probability that your problem is fixed. c. Given that your problem is fixed, find the probability that the technician with advanced training worked on your problem.

Question 8 (12 points)

State of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible? Note that only uppercase letters can be used.

Question 9 (12 Points)

Newly introduced automated production line for electric cars breaks down, on average 1.5 times per day. The breakdowns occur randomly and independent of each other. Determine the following (treat each question to be independent of other questions) -

a. What is the probability that two or more breakdowns will occur tomorrow? b. What is the probability that there will be no breakdowns at all in the next three consecutive days? c. What is the probability that there will be exactly one breakdown in three of the next seven days? d. A total of four breakdowns occurred in the last three days. What is the probability that there will no breakdown tomorrow?

Question 10 (11 points)

You are a creating a portfolio of investments for a retiring person. The portfolio consists of ten securities. Three of them must be stocks, and seven of them must be bonds. You can choose among ten stocks, and twenty bonds. Answer the following-

a. If you randomly choose ten securities, what is the probability that the portfolio specification will be met, i.e., you would have three stocks and seven bonds in the portfolio?

b. Suppose that you are told that two stocks, GM and GE must be in the portfolio. Also, you are told that bonds of ATT and Verizon must be in the portfolio. These are already in the specified set of ten stocks and twenty bonds. How likely is it that a randomly formulated portfolio of ten securities will contain these stocks and bonds, and also satisfy the requirements for containing three stocks and seven bonds?

(Note: the values in this problem are rather large to compute manually. You will be better off using Excel functions such as =permut or =combin for your analysis. If you do use them, write down the exact expressions you used as part of your analysis).