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Consider the data in Exercise 1.5 on page 13. Compute the sample variance and the sample standard deviation for both control and treatment groups. Reference Exercise 1.5: Twenty adult males between the ages of 30 and 40 participated in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control group, and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The following data show the reduction in cholesterol experienced for the time period for the 20 subjects: Control group: 7 3 -4 14 2 522 -7 95 Treatment group: -6 5 9 4 4 12 37 5 3 3 (a) Do a dot plot of the data for both groups on the same graph. (b) Compute the mean, median, and 10% trimmed mean for both groups. (c) Explain why the difference in means suggests one conclusion about the effect of the regimen, while the difference in medians or trimmed means suggests a different conclusion.Determine the debt-to-equity mix when Applied Technology bought out Southwest Semiconductor using financing as follows: $12 million from mort- gages, $5 million from retained earnings, $10 mil- lion from cash on hand, and $20 million from bonds. Business and engineering seniors are comparing methods of financing their college education dur- ing their senior year. The business student has $30,000 in student loans that come due at gradu- ation. Interest is an effective 4% per year. The engineering senior owes $50,000, 50% from his parents with no interest due and 50% from a credit union loan. This latter amount is also due at graduation with an effective rate of 7% per year. (a) What is the D-E mix for each student? (b) If their grandparents pay the loans in full at graduation, what are the amounts on the checks they write for each graduate? (c) When grandparents pay the full amount at graduation, what percent of the principal does the interest represent?1. Ten attributes were rank-ordered in terms of in- creasing importance and were identified as A, B, C, . . ., and J. Determine the weight of (a) attri- bute C and (b) attribute J. A team of three people submitted the following statements about the attributes to be used in a weighted attribute evaluation. Use the statements to determine the normalized weights if assigned scores are between 0 and 100. Attribute Comment 1. Flexibility (F) The most important factor 2. Safety (S) 70% as important as uptime 3. Uptime (U) One-half as important as flexibility 4. Rate of retum (R) Twice as important as safety Different types and capacities of crawler hoes are being considered for use in a major excavation on a pipe-laying project. Several supervisors who served on similar projects in the past have identi- fied some of the attributes and their view of rela- tive importance. For the information that follows, determine the weighted rank order, using a 0-to-10 scale and the normalized weights.An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by f(x) = [3r, r>1, elsewhere. (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 4 micrometers? Show that the n pieces of information in _ (x - ?) are not independent; that is, show that 2(n- 1) =0The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = 5(1-V)'. OSys1. elsewhere. (a) Verify that the above is a valid density function. (b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls? (c) What is the probability that a company selected at random spends more than 50% of its budget on environmental and pollution controls?Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function f(y) = 10 -#/4, 920, elsewhere. (a) Critics would certainly consider the product a bargain if it is unlikely to require a major repair before the sixth year. Comment on this by determining A(Y > 6). (b) What is the probability that a major repair occurs in the first year