september 3 2018
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Below is the summary statistics for infant mortality for 34 OECD countries. The Organization for Economic Co-operation and Development (OECD) is an international economic organization of 34 countries, founded in 1961 to stimulate economic progress and world trade.
- One of the values is larger than the others, 13. Calculate a z-score for this value and interpret its meaning. Would you consider this to be an outlier? A near outlier?
Each year the Academy of the Screen Actors Guild gives an award for the best actor and actress in a motion picture. Focus on the data for females (the sample size, n =20). The stem and leaf plot and summary statistics are given below. The sum of their age and the sum of age-squared are also given.
- Two values are relatively larger than the rest, 61 (For Helen Mirren in 2006) and 62 (Meryl Streep in 2011). Calculate z-scores for each of these values and interpret them.
- Suppose we wanted to remove the two female outliers from the data. Calculate the new mean, median, variance, standard deviation, and CV for women winners for the remaining 18 winners. Hint: subtract the values from the old sum and divide by 18. You need to square the two ages and subtract these values from the sum of squared ages. Did the outliers influence the mean and median age much? What about the variance and standard deviation?
Todd Andrlik, founder and editor of Journal of the American Revolution, wrote a piece about how young many of the founding fathers were when the Declaration of Independence was first signed in 1776. There were 56 signers of the Declaration of Independence and the descriptive statistics of their ages and the stem and leaf plot are given below.
- Describe the distribution using all the summary statistics.
- One of the values is 70 (Benjamin Franklin). Calculate a z-score for this value and interpret its meaning.
Answer the following questions about variability of data sets:
- How would you describe the variance and standard deviation in words, rather than a formula? Think of what you are calculating and how it might be useful in describing a variable.
- What is the primary advantage of using the inter-quartile range compared with the range when describing the variability of a variable?
- Can the standard deviation ever be larger than the variance? Explain.
- Can the variance ever be negative? Why or why not?
- Show the formula for the Coefficient of Variation and explain what it is and how it can be useful in comparing the variability of different variables.
Working out probabilities for flips of a coin is almost a requirement in a basic statistics course. For this problem, assume the probability of a head or tail is 0.5 and that each successive flip is independent of the previous flip.
- What is the sample space (all possible combinations) for four successive flips of a coin? Draw this out using any of the diagrams discussed in the chapter.
- Calculate the probability for two heads in four flips of a coin. How many different combinations are there?
- Calculate the probability of three tails in four flips. How many different combinations are there?
Blood comes in four types: O, A, B, and AB. The percentages of people in the United States with each blood type are shown below.
- Draw out the sample space for two people getting married with all the different combinations of blood types. Assume the two persons are independent. (Hint: The sum of the probabilities must equal 1.00.)
- What is the probability that two people getting married both have blood type O?
- What is the probability that two people getting married both have the same blood type?
- Do you think that the assumption of independence is reasonable for blood type for a couple?
A card is drawn at random from a standard 52-card deck. A deck of cards has 52 cards and four suits (hearts, diamonds, spades, and clubs).There are 13 cards in each suit (1–10, jack, queen, and king; the last three are considered face cards). Answer the following probabilities:
- The probability the card is a heart
- The probability the card is a heart or a 2
- The probability the card is black face and a face card
Joanna takes a multiple-choice quiz of four questions that is administered on a clicker in class. Each question has four possible answers (three wrong, one right). Assume the questions are independent of each other.
- Draw out the sample space for the four questions using R to stand for Right and W to stand for Wrong.
- What is the probability that she answers only one question correctly?
- What is the probability that she gets all four questions right?
- What is the probability that she gets all four questions wrong?
- What is the probability that she gets at least two questions right?
- What is the probability that she gets at least one question right?
For high school students, admission to the nation’s most selective universities is very competitive. For example, it was reported in 2007 that elite school A accepted about 12% (0.12) of its applicants, and elite school B accepted 18% (0.18). Joanna has applied to both schools. Assuming she is a typical applicant, she figures her chances of getting into both A and B must be about 2.16% (0.0216).
- How did she arrive at this conclusion?
- What additional assumption is she making?
- Do you agree with her conclusion?
- Suppose the conditional probability of getting into B, given you are already accepted into A, is 0.82. Now what is the probability of getting into both A and B?
A telemarketer who needs to make many phone calls has estimated that when he calls a prospective client, the probability that he will reach the client right away is 0.5. If he does not reach the client on the first call, the probability that he will reach the client on a subsequent call in the next half-hour is 0.15.
- What’s the probability that the telemarketer will reach his client on the second call, but not on the first call?
- What’s the probability that the telemarketer will be unsuccessful on two consecutive calls?
- What’s the probability that the telemarketer will reach his client in two or fewer calls?
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