Studies of a specific enzyme activity showed that the time the enzyme activity before complete inactivity is exponentially distributed with a mean of 12 hours. Determine the failure rate
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- Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. What is the subpopulation mean when x = 7 servings per day?Multiple myeloma, or blood plasma cancer is characterized by increased blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The data in the table below represent the bone marrow micro-vessel density for patients who had a complete response to the stem cell transplant and at the time the complete response was determined. Patient Before After 1 158 284 2 189 214 3 202 101 4 353 227 5 416 290 6 426 176 7 441 290 Please show work done by hand and/or using Excel formulas, graphing calculator unavailable. At the 0.05 level of significance, is there evidence that the mean bone marrow micro-vessel density is higher before the stem cell transplant than after the stem cell transplant?For a logistic regression looking at the log-odds of obesity among 20 to 70 year olds, age was included as a predictor. Age was recorded into categories: 20-29, 30-39. 40-49, 50-59, and 60-70. Given it is an ordinal variable, the statistician acknowledged that age could be included in the logistic regression model as continuous or categorical. Suppose that the statistician used loglikelihood ratio test of nested models to examine whether age could be treated as continuous. First, what is the null hypothesis? O Age is not a predictor of obesity Age is appropriate as a continuous variable O Age is appropriate as a categorical variable O Age is a predictor of obesity
- To determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes), a study used logistic regression. The most important explanatory variable was a labeling index (LI) that measures proliferative activity of cells after a patient receives an injection of tritiated thymidine. It represents the percentage of cells that are “labeled.” Table 4.8 shows the grouped data. Software reports Table 4.9 for a logistic regression model using LI to predict π = P (Y = 1). A. Show how software obtained π ̂ = 0.068 when LI = 8. B. Show that π ̂ = 0.50 when LI = 26.0 D. The lower quartile and upper quartile for LI are 14 and 28. Show that π ̂ increases by 0.42, from 0.15 to 0.57, between those values. E. When LI increases by 1, show the estimated odds of remission multiply by 1.16Data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. According to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 1.6 standard deviations below the mean? What is the probability that the percent change in worker output from the previous quarter is between -1.56 and 4.33?Reliability testing of the new 2.0 liter Chevy automotive engine has resulted in a time to failure distribution which is lognormal with = 90,000 mi. and s = 0.60. Find: med %3D a. R(40,000 mi.) b. MTTF and Std. Dev. c. R(90,000|40,000) d. t .90
- As a data analyst, I received requests at a rate of 1 every 25 minutes, exponentially distributed. Determine the probability that the interval between succeedingmessages is more than 1 hourThe working life time, in years, of a particular model of electric oven is exponentially distributed with mean of 8. Find the 22th percentile of the working lifetime, in years.It is known to show an exponential distribution where the average lifespan of a type of CPU is ten years. What is the probability that the company that leases the server for ten years will encounter a central processing unit failure within the period of use?
- The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).Out of 100 patients, 41 were not cured and 59 were cured. The 41 not cured, 25 were not given treatment and 16 were given. Of 59 cured, 22 were not given treatment and 37 were given treatment. If control condition is no treatment given then slope of logit is equal to?"If the iron cutting machine in a factory works continuously for a certain period of time under the same conditions, it goes into malfunction. In this type of failure, the machine takes 24 hours to cool down. After the machine has cooled down, it continues to work the next day. Assume that the running time (minutes) of this machine until it malfunctions has a normal distribution. The working time of the iron cutting machine until the failure was measured for 9 different days, which were chosen at random. Continuous working time (minutes): 14-26-18-29-12-19-22-30-19 a) Establish the 95% confidence interval for the average uninterrupted working time of this iron cutting machine and interpret the result.b) The factory chief claims that the average continuous operating time of the machine is less than 23 minutes. Test the claim that the average continuous working time of this iron cutting machine is less than 23 minutes at the 0.05 significance level and the result isPlease comment.
