We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when µ = 1680 cycles.

SOLVE STEP BY STEP IN DIGITAL FORMAT XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 8. If the daily production of a factory machine has more than 10% defective items, it is necessary to repair it. A random sample of 100 parts from the day's production contains 15 defective parts, and the supervisor decides that the machine needs to be repaired. Does the sample evidence support your decision? Use a test with level 0.01

Ankylosing spondylitis is an inflammatory disease which affects the spine and sacroiliac joint and can lead to the fusing of vertebrae in the spine. Exercise is important in helping manage pain, therefore a pharmaceutical company wanted to test if their new biologic would increase the time a patient could exercise before experiencing discomfort. The following table gives the time (in minutes) seven patients were able to exercise before reporting pain, both at baseline and then again after six months of taking the biologic.Exercise Time (in minutes)Subject 1 Baseline 30 Post-treatment 40Subject 245 40Subject 350 60Subject 435 37Subject 555 60Subject 620 25Subject 775 75Assume the population(s) of all exercise times is (are) normally distributed. Use JMP to test whether the evidence suggests that the time a person with ankylosing spondylitis can exercise before experiencing discomfort increases after taking this new biologic. Validate the test statistic from JMP by computing it manually.…

A study published in JAMA in 2004 examined past results of other studies on bariatric surgery.  Bariatric surgery is done to replace the size of the stomach in various ways.  It is typically used on only obese patients,  and one the traditional form of the surgery,  gastric bypass has a 1% mortality (death) rate caused by surgery.  However,  in the studies reporting on the effects of the surgery on Type ll diabetes,  1417 of 1846 diabetic patients recovered completely from diabetes after surgery.  These patients no longer need medication like insulin (which is injected into the skin) or pills to help manage blood sugar.  In a study released a decade later,  the percentage of patients who recover from diabetes has increased 80%. Using confidence intervals determine whether this is a significant change from the 2004 data. Use n=2000

It has been hypothesized that allergies result from a lack of early childhood exposure to antigens. If this hypothesis were true, then we would expect allergies to be more common in very hygienic households with low levels of bacteria and other infectious agents. To test this theory, researchers at the University of Colorado sampled the houses of 61 children 9-24 months old and recorded two variables: (1) whether the child tested positive for allergies and (2) the concentration of bacterial endotoxin in the house dust (endotoxin units per ml, EU/ml)1. The following are the endotoxin levels at the homes of the 51 children tested negative for allergies.  708.23  911.60  976.81  1316.63  262.74  9772.08  370.76  229.16  2570.51891.19  3163.20  1777.65  1288.57  436.23  2631.63  1173.52  911.67  7942.42  740.32  356.92  1175.48  1480.55  2754.61  575.62  573.89  468.26 1000.71  364.22  1025.26  1022.04  645.41  363.57  977.47  1022.75  1860.63 371.13  174.73  399.68  1479.77  2882.96…

Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal). The results were as follows:     Duration of Exposure   <1 1 to <5 ≥5 Diseased 14 13 18 Sensitized 11 20 15 Normal 78 140 209 Test the hypothesis of independence. Use the a=0.10 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude? State the null and alternate hypotheses.

A study published in JAMA in 2004 examined past results of other studies on bariatric surgery.  Bariatric surgery is done to replace the size of the stomach in various ways.  It is typically used on only obese patients,  and one the traditional form of the surgery,  gastric bypass has a 1% mortality (death) rate caused by surgery.  However,  in the studies reporting on the effects of the surgery on Type ll diabetes,  1417 of 1846 diabetic patients recovered completely from diabetes after surgery.  These patients no longer need medication like insulin (which is injected into the skin) or pills to help manage blood sugar.   If you had a morbidly obese relative with diabetes what would you tell him or her about bariatric surgery? Explain. Would you recovered it? Why/ why not?