1.Purchasing microchips. An important component of your desktop or laptop personal computer (PC) is a microchip. The table gives the proportions of microchips that a certain PC manufacturer purchases from seven suppliers.
a.It is known that the proportions of defective microchips produced by the seven suppliers are .001, .0003, .000–. .006, .0002, .0002, and .001, respectively. If a single PC microchip failure is observed, which supplier is most likely responsible?
b.Suppose the seven suppliers produce defective microchips at the same rate. .0005. If a single PC microchip failure is observed, which supplier is most likely responsible?
2. Bridge inspection ratings. According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated every 2 years. The NBIS rating scale ranges from 0 (poorest rating) to 9 (highest rating). University of Colorado engineers used a probabilistic model to forecast the inspection ratings of all major bridges in Denver (Journal of Performance of Constructed Facilities, Feb. 2005). For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.
a.Use the forecast to find the probability that in a random sample of 10 major Denver bridges, at least 3 will have an inspection rating of 4 or below in 2020.
b.Suppose that you actually observe 3 or more of the sample of 10 bridges with inspection ratings of 4 or below in 2020. What inference can you make? Why?
3.Employees’ choices of health care plans. Most companies offer their employees a variety of health care plans to choose from e.g., preferred provider organisations (PPOs) and health maintenance organisations (HMOs). A survey of 100 large. 100 medium, and 100 small companies that offer their employees HMOs, PPOs, and fee-for-service plans was conducted: each firm provided information on the plans chosen by their employees. These companies had a total employment of 833,303 people. A breakdown of the number of employees in each category by firm size and plan is provided in the table.
One employee from the 833.303 total employees is to he chosen at random for further analysis. Define the events A and B as follows:
- A:(Observe an employee that chose fee-for-service)
- B:(Observe an employee from a small company)
b.Find P(A ∩ B)
c.Find P(A ∪ B)
d.Find P (A\B)
e.Are A and B independent?Justify your answer.
4. Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were diagnosed with latex allergy based on a skin-prick test reported on their exposure to latex gloves (Current Allergy & Clinical Immunology, Mar. 2004). Summary statistics for the number of latex gloves used per week are = 19.3, s = 11.9.
a.Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.
b.Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.
c.Give a practical interpretation of the interval, part b
d.Give the conditions required for the interval, part b, to be valid.
5. A new dental bonding agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smartbond) has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive (Trends in Biomaterials & Artificial Organs, Jan. 2003). Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of .7 = 5.07 Mpa and a standard deviation of s = .46 Mpa. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive.
a.Set up the null and alternative hypotheses for the test
b.Find the rejection region for the test using α= .01.
c.Compute the test statistic.
d.Give the appropriate conclusion for the test.
e.What conditions are required for the test results to be valid?