1. In one city, 23% of the population is under 25 years of age. Three people are selected at random from the city. Find the a one- probability distribution of X, the number among the three that are under 25 years of age. x| P(X = x) 0.23 2 0.0529 3 0.0122 x| P(X = x) O 0.4565 x|P(X = x) 0.4565 x| P(X = x) O 0.4565 1 0.1364 1 0.4091 1 0.4091 0.0407 0.1102 2. 0.1222 3 0.0122 3 0.0242 0.0122
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- In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normalResistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?
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- A pharmaceutical company has developed a new drug to help relieve acid reflux. However, as with all new drugs, there are concerns about adverse side effects. To check this, the company administers the drug to n randomly chosen people with acid reflux, and it finds that k of them experience adverse side effects. The company hopes to reject the null hypothesis that the proportion of drug-takers who experience adverse side effects is at least 0.5%. Which of the following is true? a. If n=1,250 and k=1, this is enough evidence to reject the null at the 1% level. b. If n=1,000 and k=3, this is enough evidence to reject the null at the 10% level. c. If n=4,000 and k=9, this is enough evidence to reject the null at the 1% level. d. If n=1,600 and k=4, this is enough evidence to reject the null at the 5% level.A certain university claims that for the last school year the proportion of students who were not able to earn a college diploma is at most 25%. What is the null hypothesis? a. Proportion is greater than or equal to 0.25.b. Proportion is less than or equal to 0.25.c. Proportion is equal to 0.25.d. Proportion is not equal to 0.25.A certain university claims that for the last school year the proportion of students who were not able to earn a college diploma is at most 25%. What is the alternative hypothesis? a. Proportion is greater than or equal to 0.25.b. Proportion is less than or equal to 0.25.c. Proportion is equal to 0.25.d. Proportion is not equal to 0.25.