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- The Segment-Addition Postulate can be generalized as follows: The length of a line segment equals the sum of the length of its parts. State a general conclusion regarding AE based on the following figure.Suppose that 95% of the bags of certain fertilizer mix weigh between 49 and 53 pounds. Averages of three succesive bags were plotted, and 47.5% of these were observed to lie between 51 and X pounds. Estimate the value of X. State assumptions you make and say whether these assumptions are likely to be true for this example.Consider that a researcher is attempting to reduce the expected distance between M and µ as much as possible when conducting a research study. One thing they can do is _____.
- A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at most 21 grams was y1 = 28 for the day shift and y2 = 11 for the night shift. Let p1 and p2 denote the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively. a) Give a point estimate for p1-p2 b) Find and interpret a 95% confidence interval for p1-p2 c) Can you claim a difference between difference between proportions of mints that weight at most 21g for the day and night shifts?Suppose that a researcher is interested in the average standardized test score for fifth graders in a local school district. The fifth graders at a specific school would comprise a ___________ and their average test score would be a ___________.The demand for a commodity is given by Q = β0 + β1P + u, whereQ denotes quantity, P denotes price, and u denotes factors other thanprice that determine demand. Supply for the commodity is given byQ = ϒ0 + ϒ1P + v, where v denotes factors other than price that determinesupply. Suppose that u and v both have a mean of zero, have variancesσ2u and σ2v, and are mutually uncorrelated.a. Solve the two simultaneous equations to show how Q and P dependon u and v.b. Derive the means of P and Q.c. Derive the variance of P, the variance of Q, and the covariancebetween Q and P.d. A random sample of observations of (Qi, Pi) is collected, and Qi isregressed on Pi. (That is, Qi is the regressand, and Pi is the regressor.)Suppose that the sample is very large. i. Use your answers to (b) and (c) to derive values of the regressioncoefficients. ii. A researcher uses the slope of this regression as an estimate of theslope of the demand function (β1). Is the estimated slope too largeor too small?
- The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of the canteen arrive at an average of 50 an hour. Suppose that management wants to evaluate the desirability of opening a second order-processing station so that two customers can be served simultaneously. Assume a single waiting line with the first customer in line moving to the first available server. a. What is the average arrival time in minutes of customers? b. What is the average service time in minutes of the canteen? c. What is the probability that the canteen has a customer?The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.A person who is exercising should exceed his or her maximum heart rate, which is determined on the basis of that person’s sex, age, and resting heart rate. The following table relates resting heart rate and maximum heart rate for a 20 year old man. Resting heart rate (in beats per minute) Maximum heart rate (in beats per minute) 50 166 60 167 70 171 80 172 Using a 5% level of significance, test the claim that B>0
- The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x=104.18, y=105.25, r=0.892, P-value=0.000, and y=17.77+0.84x, where x represents the IQ score of the younger child. Find the best-predicted value of y given that the younger childhas an IQ of 108? The best-predicted value of y is?Given a set of points, the least-squares line formed by letting xbe the independent variable will not necessarily be the sameas the least-squares line formed by letting y be the independentvariable. Give an example to show why this is true.
