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1. In pregnancy, women often undergo screening to assess if their fetus has Down Syndrome. The screening test evaluates levels of hormones in the blood and results are reported as positive or negative. A sample of 2548 pregnant women undergo the test and each woman is followed to birth to determine if the fetus was affected with down syndrome. The results of the screening tests are summarized below. Use this information to answer questions 1 - 5.
- Question 1 0.3/0. HW 8 Question 1: Calculate the False Positive Rate. Your Answer: 0.
- Question 2 0.3/0. HW 8 Question 2: Calculate the Specificity of the test. Your Answer: 0.
- Question 3 0.3/0. HW 8 Question 3: Calculate the False Negative Rate. Your Answer: 0.
- Question 4 0.3/0. HW 8 Question 4: Calculate the Sensitivity of the test. Your Answer: 0.
- Question 5 0.3/0.
HW 8 Question 5: Do you feel that this is a good test? Show answer choices The test is not good. The specificity is really low. Overall, the test is pretty good. The specificity and sensitivity of the test are both above 90%. The test is perfect. There is no error included. The test is not good. The sensitivity is really low.
- Question 6 0.3/0. HW 8 Question 6: What is wrong with the following probability distribution? Show answer choices The probability values must sum to be 0 The probability values must all be less than 0 or greater than 1 The probability values must sum to be 1 The probability values must all be between 0 and 1 and here P(Red) = -0.
- Question 7 0.3/0. HW 8 Question 7: Given the following table, what must the probability of getting an A in the class be? Your Answer: 0. 9. Suppose the discrete random variable of interest, x , is the number of rolls that result in a composite number when rolling a die three times ( and 6 are the possible composite numbers when rolling a die). Use this scenario to answer questions 8 - 15.
- Question 8 0.3/0.
HW 8 Question 11: Create the probability distribution for x (the number of times a composite number is rolled when rolling a die three times). HW 8 Question 12: To verify this is a valid discrete probability distribution, what properties must be satisfied? Show answer choices All the above
- Question Show answer choices
- 0.3/0.
- Your Answer: HW 8 Question 9: How many outcomes are there in the tree diagram?
- Question
- 0.3/0.
- P(CCC) = 0. Show answer choices
- P(CCN) = 0.
- P(CNC) = 0.
- P(CNN) = 0.
- P(NCC) = 0.
- P(NCN) = 0.
- P(NNC) = 0.
- P(NNN) = 0.
- P(CCC) = 0.
- P(CCN) = 0.
- P(CNC) = 0.
- P(CNN) = 0.
- P(NCC) = 0.
- P(NCN) = 0.
- P(NNC) = 0.
- P(NNN) = 0.
- P(CCC) = 0.
- P(CCN) = 0.
- P(CNC) = 0.
- P(CNN) = 0.
- P(NCC) = 0.
- P(NCN) = 0.
- P(NNC) = 0.
- P(NNN) = 0.
- Question
- 0.3/0.
- P(0) = 0. Show answer choices
- P(1) = 0.
- P(2) = 0.
- P(3) = 0.
- P(0) = 0.
- P(1) = 0.
- P(2) = 0.
- P(3) = 0.
- P(0) = 0.
- P(1) = 0.
- P(2) = 0.
- P(3) = 0.
- P(0) = 0.
- P(1) = 0.
- P(2) = 0.
- P(3) = 0.
- Question
- Question The random variable x must be discrete
HW 8 Question 13: Calculate the mean (expected value) for x. Your Answer: 1
- Question 14 0.3/0. HW 8 Question 14: Calculate the variance for x. Your Answer: 0.
- Question 15 0.3/0. HW 8 Question 15: Calculate the standard deviation for x. Your Answer: 0. 18. We will consider a simple lottery wager, the straight from a pick 3 game. You pay $0.50 and choose a three-digit number. The state chooses a three-digit winning number at random and pays $250 if your number is chosen. Because there are 1000 three-digit numbers, you have probability 1/1000 = 0.001 of winning. Below is the discrete probability distribution for the winnings. Use this information to answer questions 16 - 18.
- Question 16 0.3/0. HW 8 Question 16: Calculate the mean of x. Your Answer: 0.
- Question 17 0.3/0. HW 8 Question 17: Calculate the variance of x.
Use StatCrunch to calculate probabilities for this discrete probability distribution and enter the values below.
- Question 23 0.1/0. HW 8 Question 20a: P(X=0) = Your Answer: 0.
- Question 24 0.1/0. HW 8 Question 20b: P(X=1) = Your Answer: 0.
- Question 25 0.1/0. HW 8 Question 20c: P(X=2) = Your Answer: 0.
- Question 26 0.1/0. HW 8 Question 20d: P(X=3) = Your Answer: 0.
- Question 27 0.1/0. HW 8 Question 20e: P(X=4) = Your Answer: 0.
- Question 28 0.1/0. HW 8 Question 20f: P(X=5) =
Your Answer: 0.
- Question 29 0.1/0. HW 8 Question 20g: P(X=6) = Your Answer: 0.
- Question 30 0.1/0. HW 8 Question 20h: P(X=7) = Your Answer: 0.
- Question 31 0.1/0. HW 8 Question 20i: P(X=8) = Your Answer: 0.
- Question 32 0.1/0. HW 8 Question 20j: P(X=9) = Your Answer: 0.
- Question 33 0.1/0. HW 8 Question 20k: P(X=10) = Your Answer: 0. 39. HW 8 Question 21: Once again, suppose we are interested in the variable X which represents the number of tails flipped when flipping a coin 3 times.
- Question 34 0.2/0.
43. HW 8 Question 22: For the discrete probability distribution created in question 19 calculate the following (use the formulas presented in class).
- Question 37 0.3/0. HW 8 Question 22a: Mean Your Answer: 1.
- Question 38 0.3/0. HW 8 Question 22b: Variance Your Answer: 0.
- Question 39 0.3/0. HW 8 Question 22c: Standard Deviation Your Answer: 0. 47. HW 8 Question 23: When we know the discrete probability distribution has certain properties, sometimes there are shortcut formulas for calculating probabilities, means, variances, and standard deviations. In this case the discrete probability distribution is binomial. For the binomial the shortcut formula for the mean is and the variance is (where ). In the examples presented in the previous questions, n is the number of flips, p is the probability of getting tails on a single flip, and q is the probability of not getting tails on a single flip. Using these shortcut formulas calculate the following.
- Question 40 0.3/0. HW 8 Question 23a: Mean of the probability distribution in question 19. Your Answer: 1.
- Question 41 0.3/0.
HW 8 Question 23b: Variance of the probability distribution in question 19. Your Answer: 0.
- Question 42 0.3/0. HW 8 Question 23c: Standard Deviation of the probability distribution in question
Your Answer: 0. - Question 43 0.3/0. HW 8 Question 23d: Does the shortcut formulas used in parts a, b, and c above give you the same result as question 22? Show answer choices Yes, the shortcut formulas is an easier way to get the mean, variance, and deviation. No, the shortcut formulas do not work.
- Question 44 0.3/0. HW 8 Question 23e: Mean of the probability distribution in question 20. Your Answer: 5
- Question 45 0.3/0. HW 8 Question 23f: Variance of the probability distribution in question 20. Your Answer: 2.
- Question 46 0.3/0. HW 8 Question 23g: Standard Deviation of the probability distribution in question
Use the shortcut formulas introduced in question 23 to calculate the following for X. ( n is the number of rolls, p is the probability of getting a six on a single roll, and q is the probability of not getting a six on a single roll)
- Question 50 0.2/0. HW 8 Question 25a: Mean Your Answer: 1.
- Question 51 0.2/0. HW 8 Question 25b: Variance Your Answer: 1.
- Question 52 0.2/0. HW 8 Question 25c: Standard Deviation Your Answer: 1.
- Question 53 0.2/0. HW 8 Question 26: Compare the descriptive statistics for the variables Coin3, Coin10, Die3, and Die10 to the mean and standard deviation calculated in question 23, 24, and 25. Explain the similarities and differences between the descriptive statistics for these variables and those calculated in questions 23, 24, and 25. As you compare the results, think about this scenario in regards to inferential statistics. The values calculated in questions 23, 24, and 25 are parameters (from the population) and the values in the descriptive statistics from the student survey data are statistics (from a sample). Show answer choices The table above gives the population parameters along with statistics that could be used to estimate them. As expected the statistics are exactly equal to the parameters. There is no error when doing inferential statistics. The table above gives the population parameters along with statistics that could be used to estimate them. As expected the statistics are close to the parameters, but not exactly equal. Through the random sampling process we know there will be error in the estimates.
