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- 4. A spinner is now created with four equal sized sectors as shown, An experiment is run where the spinner is spun twice and the outcome is recorded each time. (a) Create a sample space list of ordered pairs that represent the outcomes, such as (4, 2), which represent spinning a 4 on the first spin and a 2 on the second spin. 3 2 (b) Using your answer from (a), determine the probability of obtaining two numbers with a sum of 4.4. A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 200 house purchases in the current year were randomly selected and 80 of those were made by singles. In the second study, again 200 house purchases were randomly selected from 5 years ago and 57 of those were made by single people. Test the newspaper's claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper's claim? Let singles now be Population 1 and let singles 5 years ago be Population 2. Step 1. State the null and alternative hypotheses for the test. Fill in the blank below. A) Step 2. Compute the value of the test statistic. Round your answer to two decimal places. Step 3. Draw a conclusion and interpret the decision. A) We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level…3-49. The number of rescue calls received by a rescue squad in a city follows a Pois- n distribution with u = 2.83 per day. The squad can handle at most four calls a day. son
- A single strand of a DNA molecule is a sequence of nucleotides. There are four possible nucleotides in eachposition (step), one of which is cytosine (C). In a particular long strand, it has been observed that C appearsin 34.1% of the positions. Also, in 36.8% of the cases where C appears in one position along the strand, italso appears in the next position.1. What is the probability that a randomly chosen pair of adjacent nucleotides is CC (that has cytosinein both locations).2. If a position along the strand is not C, then what is the probability that the next position is C?3. If a position n along the strand is C, what is the probability that position n + 2 is also C? How aboutposition n + 4?4. Answer parts (a)- (c) if C appeared independently in any one position with probability 0.341.5. a) Suppose you have three coins in a bag: the first coin is fair, with prob- ability of HEAD (H) equals to that of TAIL (T), i.e., P(X = H|M1) = P(X = T|M1), where X is a binary random variable representing HEAD or TAIL. The second is a loaded coin with P(X = takes a coin out of the bag at random and flips it. When it lands, you observe that the side of the coin facing up is HEAD. What is the probabilities that this is the first, second and third coin? Hint: You may assume the three coins are equal likely to be selected from the bag, i.e., P(M1) = P(M2) = P(M3) = , and you need to calculate P(M||X = H), P(M2|X = H) and P(M3|X = H). H|M2) = 0.8. The third is also a loaded coin with P(X = Н Мз) — 0.2. Your friend 6) What if we don't know the probabilities of HEAD for each coin? Design an iterative algorithm using pseudo-code to estimate these probabilities.1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39
- 3. An urn contains exactly 10 red chips and 6 blue chips. Five chips are randomly selected without replacement. Let X denote the number of blue chips in the sample of five chips. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) (b) What is the probability that there are between two and four blue chips among the five chosen chips? Express your answer as a decimal. = (*)*3. The paper "Effects of Caffeine on Repeated Sprint Ability, Reactive Agility Time, Sleep and Next Day Performance"† describes an experiment in which male athlete volunteers who were considered low caffeine consumers were assigned at random to one of two experimental groups. Those assigned to the caffeine group drank a beverage which contained caffeine 1 hour before an exercise session. Those in the no-caffeine group drank a beverage that did not contain caffeine 1 hour before an exercise session. That night, participants wore a device that measures sleep activity. The researchers reported that there was no significant difference in mean sleep duration for the two experimental groups. In the context of this experiment, explain what it means to say that there is no significant difference in the group means. A) The difference in mean sleep duration for the caffeine and no-caffeine groups could have occurred by chance just due to the random assignment, assuming there is a real difference…
