AP Statistics Unit 5

In a simple random sample of 100 households in 2000, 43 had some credit card debt. In another simple random sample of 150 households in 2012, 72 had some credit card debt. Which of the following is the correct test statistic for testing the hypothesis H₀ : p_{2012 =} p₂₀₀₀ , that there is no difference in the proportion of households with credit card debt in these two years?

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In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model. They base these estimates on both the value of the car and how much damage it sustains in accidents.

Let C be a random variable that represents the cost of claims on a randomly selected car of one particular model. The probability distribution for C is given at left (see image).

Calculate the MEAN and the STANDARD DEVIATION of C.

(15 points) Sarah is packing a basket to bring to a Friends-giving picnic. She is bringing a turkey sandwich, a pecan pie, and a gallon of apple cider. Depending on preparation she estimates that the sandwich will weigh an average of 8.8 oz with a standard deviation of 0.6 oz, the pecan pie will weigh an average of 32.4 oz with a standard deviation of 1.6 oz, and the gallon of apple cider will weigh an average of 128 oz with a standard deviation of 0.2 oz. Let W be the total weight of the items that Sarah is bringing to the picnic. Calculate the mean and the standard deviation for W. Show your work, use SQRT(#) to show that you are taking square roots (if needed), and interpret your answer in context.

(15 points) What are the four characteristics of a Binomial Random Variable? What are the four characteristics of a Geometric Random Variable? Briefly explain all of the characteristics in your response.

(15 points) A student did not study for the Multiple Choice AP Stats Quiz. Assume that each question is independent, and that there is a 20% probability for a randomly selected unprepared student to correctly guess an answer to a question. Let X be the number of questions that a randomly selected unprepared student correctly guesses on the quiz. If there are 10 questions on the multiple choice quiz, what is the probability that a randomly selected unprepared student guesses at least 6 questions correct? Explain how you got your answer.

• finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn't convincing evidence that a majority supports the increase.
• finds convincing evidence that a majority of residents supports the tax increase, when in reality at most 50% of city residents support the increase.
• finds convincing evidence that a majority of residents supports the tax increase, when in reality more than 50% of city residents do support the increase.
• does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than 50% of city residents do support the increase.
• does not find convincing evidence that a majority of residents supports the tax increase, when in reality at most 50% of city residents do support the increase.

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