Example 16. Compute Fisher's Ideal Index number from the data given below and show that it satisfies the Time Reversal and Factor Reversal Tests. Base Year Current year Item Оиаntity Price Оuantity Price A 12 10 15 12 В 15 7 20 5 24 5 20 D 5 16 5 14
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- Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 55 clam shells in February and 55 clam shells in March. 14 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months; specifically, if the population proportion in February is higher than March. Let ? = 0.1.Note: Do all calculations as February - MarchA) The point estimate for the true difference in proportion of dark growth bands between February and March is: Note: answer using 4 decimal precisionB) The test statistic, ztest, is: Note: answer using 2 decimal…Suppose in a Country Waffleland, there are two socio-economic classes. The workingclass accounts for 90% of the population. Each person in the working class has awealth of w, where w > 0. The rest of the society consists of people with inheritedwealth. Each person in this class has a wealth of 9w. What is the Gini coefficientof the wealth distribution in this country?1.) This is an Econ - Econometrics question: Let arr86 be a binary variable equal to 1 if a man was arrested during 1986, and zerootherwise. You have a dataset of young men from California who were born in 1960 or1961 and have at least one arrest prior to 1986. You also have data on the proportion ofprior arrests that led to a conviction (pcnv), the average sentence served from priorconvictions in months (avgsen), months spent in prison since age 18 prior to 1986(tottime), months spent in prison in 1986 (ptime86), and the number of quarters (0 to 4)that the man was legally employed in 1986 (qemp86). You estimate the following linearprobability model (standard errors are in parentheses): arr86 = 0.441 - .162pcnv + .0061avgsen - .0023tottime(.017) (.021) (.0065) (.005) - .022ptime86 - .043qemp86(.005) (.005) n= 2725R2=.0474 a) Interpret the coefficient on avgsen, commenting on both magnitude and significance. Based on these results, do longer sentences deter future crime? b) What is the…
- Imagine that before the debate, a sample of 75 likely voters had 41 who preferred candidate A. After the debate, a separate sample of 75 likely voters had 34 who preferred candidate A. Determine if the support for candidate A decreased after the debate, using alpha=0.10. By hand.M:14) Using Ordinary Generating Functions prove in how many ways the sum of 5 dices give n as a result?In a certain industry, roughly 40% of managers have an advanced degree (Master's or beyond). From a group of 10 managers, X represents the number of them who have an advanced degree. What model is most appropriate for X? A. Poisson B. Binomial C. Binomial with n=10 and p=0.40 D.Poisson with λ = 4
- In a certain industry, roughly 40% of managers have an advanced degree (Master's or beyond). From a group of 10 managers, X represents the number of them who have an advanced degree. What model is most appropriate for X? A. Poisson B. Binomial C. Binomial with n=10 and p=0.40 D. Poisson with λ=4λ=4In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) What is ?? b) Write out the formula for the probability distribution of the random variable r. P(r) = _________ c) Find the probability that one otter will initiate social grooming four or more times during the 30-minute observation period. (Round your answer to four decimal places.)In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) Find the probabilities that in your 30 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) = b) Find the probability that one otter will initiate social grooming less than four times during the 30-minute observation period. (Round your answer…
- In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 40 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 40-minute interval) one otter initiates social grooming of another. Lambda = 6.8 (b) Find the probabilities that in your 40 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) =In a certain year,27% of adults in a certain country viewed a college education as essential for success. For the following ten-year period, this percentage increased by approximately 2.6percent each year. The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by ________.Everyday, James reverses his car from his driveway on to the road in such a way that there is a very small probability P that his car will be involved in a collision. ( i) Show that the probability that there will be no collision in a five-day week is (1−P)^5 and state one assumption that is made in your answer. (iii) Let P = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that James will avoid a collision in 500 days.
