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- Sports shirts are frequently classified as S, M, L, XL for small, medium, large and extra-large neck sizes. S fits a neck circumference of less than 37cm, M fits between 37 and 40.5cm and L fits between 40.5cm and 44cm while XL fits necks over 44cm in circumference. The neck circumference of adult males has a normal distribution with µ = 40cm and σ = 2cm. (i) What proportion of shirts should be manufactured in each category? (ii) If you wanted to define categories S, M, L, XL so that the categories con- tained 20%, 30%, 30% and 20% respectively, of the total population of adult males, what neck sizes must you assign to each of the categories?A boat capsized and sank in a lake. Based on assumption of mean weight of 131 lb, the boat was rated to carry 70 passengers (so the load limit was 9,170 lb). After the boat sank, the assumed mean weight for similar boats was changed from 131 lb to 173 lb. Complete parts a and b below A. Assume that a similar boat is loaded with 70 passengers, and assume that the weight of people are normally distributed with a mean of 180.7 lb and a standard deviation of 39.2 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 131 lbA yogurt producer claims the variance on their yogurt containers is 4 grams or less . A sample of 30 containers had a sample variance of 9 grams. We want to test if the variance is greater than 4 (a=0.05) The correct alternative hypothesis to test the producer claim is : Select one: O a. HA :02 s4 O b. HA :02 > 16 29 O C. HA :02 > 4 36 O d. Ho :02 > 2 Finis e Next page
- Q. Suppose, in an exam there are two parts in the question paper that are part A and part B. Let us assume that, X and Y represent the marks obtained in part A and part B respectively. The joint distribution of X and Y are given below: Y p(x.y) Y = 0 Y = 5 Y = 10 Y = 15 X = 0 0.02 0.06 0.02 0.10 X = 5 0.04 0.15 0.20 0.10 X = 10 0.01 0.15 0.14 0.01 a. If the total marks are obtained by adding the marks obtained in the two individual parts of the question paper then find the expected marks, E[X,Y] obtained by a randomly selected student. b. If the maximum marks of the two parts are recorded then what is the expected recorded marks? Write your answer in the script, convert into pdf and then submit the pdf on the provided link at the end. (Not here)One property of the F-distribution used for the Analysis of Variance is thatA. It is symmetric.B. The exact shape of the F-distribution depends on two different degrees of freedom.C. Values of the F-distribution can be negative.D. The total area under the curve is equal to 2.b.
- A researcher in a scientific foundation wished to evaluate the relation between intermediate and senior level annual salaries of research mathematician (Y, in thousand dollars) and an index of publication quality (X1), the number of years experience (X2), and an index of success in obtaining grant support (X3). A. Determine the R2 and adjusted R2. B. Determine the significant factors. C. Determine if the residual follows a normal distribution . Determine if the variance is constant over time. Find the leasts-squares regression equation. The data for a sample of 24 intermediate and senior level research mathematicians follow.4. In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 21 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm°. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x = 8.14 cm ands = 0.8 cm³. Conduct the appropriate test at the a = 0.01 level of significance. State the null and alternative hypotheses. Ho: H (1) H1: µ (2) (Type integers or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. (3) the null hypothesis. There (4) sufficient evidence to claim that the mean hippocampal volume is (5) cm³. 33) Do people drive more slowly on tree-lined street? In the following table x is a random variable representing the number of tree per mile of road on randomly selected streets with a 25 mph speed limit in a major city while y represents the average speed of cars in mph sampled over a one-hour period at the same time of day 47 25 12 30 me to que 35 y 25 50 44 45 ent brit (d a) Draw a Scatter Plot Diagram of the data. Remember to label the axes appropriately and nsbnee sigmse eris bnit or slummot choose a consistent scale. cins2 oinutonomodgo2 nemdeent b) Based on the Scatter Plot Diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative: 4) Professor Wan is in charge of a program to prepare people for a high-school equivalence exam. Records show that 70% of the students need work in math, 60% need work in English, and 50% need work in both areas. Use the appropriate formula to compute the probability that a student selected at random will need…
- 2 In building electronic circuitry, the breakdown voltage of diodes is an important quality char- Acteristic. The breakdown voltage of 12 diodes were recorded as follows (in volta): 9.099 9.174 9.327 9.377 8.471 9.575 9.514 8.928 8.800 8.920 9.913 8.306 Solution A quality engineer claimed that the variability of the breakdown voltage is not less than 0.55. Can the data support the engineer's claimed at a 0.057 ii. If level of significance is reduced to 0.02, will you change the conclusions you have made in (i)? Justified your answer.answer d)The total expenses of a hospital (dependent variable) are related to many factors. One of these factors is the number of admissions to the hospital (independent variable). Using the summary output below to answer, what is the meaning (analysis) of the coefficient of determination? SUMMARY OUTPUT Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Statistics Regression Residual Total df 0.98706 0.974288 0.972145 8.106794 Coefficients 14 1 12 13 SS 29883.07 788.6412 30671.71 Standard Error Intercept 1.518053 Admissions 0.668591 OA) is the value of Expenses with one unit increase in Admissions 3.248929 0.031354 MS 29883.07 65.7201 t Stat 0.467247 21.32375 F 454.7022 P-value 0.648693 6.59E-11 Significance F 6.59E-11 Lower 95% -5.56075 0.600276 Upper 95% 8.59686 0.736907
