IHP 525 Quiz Two

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Southern New Hampshire University **We aren't endorsed by this school
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IHP 315
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Statistics
Date
Aug 9, 2023
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IHP 525 Quiz Two 1. A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time. a. True or False: Each call is an independent random event. In two attempts, what is the probability of achieving...... True, each of the calls is a random event . b. exactly two successful calls? (success = reach a live person) n=2 p=0.15 p(x=2) = (2/2) x (0.15 2) x (0.85 0) = 0.0225 0.0225 = 2.25% c. one success and one failure (in any order)? P(x=1) = (2/1) x (0.85 1) = 0.255 P(x=1) = (0.15 x 0.85) + (0.85 x 0/15) = 0.1275 + 0.1275 = 0.255 = 25.5% 2. The prevalence of a trait is 76.8%. In a simple random sample of n = 50, how many individuals are expected to exhibit this characteristic and what is the corresponding standard deviation of this estimate? P = 76.8% = 0.768 Q = 1 - p = 1 - 0.768 = 0.232 N = 50 n x p = 50 x 0.768 = 38.4 Sd = square root n x p x q = square root of 50 x 0.768 x 0.232 = square root . 9088 = 2.9847 = 2.985 3. Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with Salmonella . If Salmonella contamination occurs independently within and between egg cartons and Linda makes a three-egg omelet, what is the probability that her omelet will contain at least one Salmonella contaminated egg? P = 1/6 = 0.1666 Q = 1 - p Q = 1 - 0.1666 = 0.8334 P (x ≥ 1) = 1- p (x = 0) = 1 - (.833)3 = 1 - .578 = 0.422 = 42.2%
4. Suppose that heights of 10-year-old boys vary according to a normal distribution with µ = 138 cm and σ = 7 cm. What proportion of 10-year-old boys is less than 140 cm in height? Z - score = µ = 138 o = 7 cm z = (x - µ) / o Z = (140-138)/7 Z = 2/7 Z = 0.2857 P (Z<0.2857) = 0.612 = 61.2% 5. A survey selects a simple random sample of n = 500 people from a town of 55,000. The sample shows a mean of 2.3 health problems per person. Based on this information, say whether each of the following statements is true or false . Explain your reasoning in each instance. No calculations necessary. a. It is reasonable to assume that the number of health problems per person will vary according to a normal distribution. False, because the variable does not follow the normal distribution when the mean of sampling distribution does. b. It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution. True, because the sample size is large to where it can produce a normal distribution.
6. A simple random sample of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately normally distributed with σ = 2.8 inches. Conduct a two- sided hypothesis test to determine whether the male students have heights that are significantly different than expected. Show all hypothesis testing steps. Hypothesis: Ho: µ = 69 versus Ha: µ ≠ 69 Test Statistic: Zstat = 1.52 P = Pr(z≥1.52) = 0.0643 µ = 60 o = 2.8 n = 18 x = 70 one sided two sided o/square root of n p = 2(0.643) 2.8/square root of 18 = 2.8/4.24 = 0.66 p = 0.1286 Z stat = (x - µ)/o = (70-69)/ 2.8 = 1/0.66 = 1.515 = 1.52 It is considered nonsignificant by usual conventions. 7. True or false? The p -value refers to the probability of getting the observed result or something more extreme assuming the null hypothesis True, because the P-value explains the rejection area for the null hypothesis.
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