What Is Testing? The terms hypothesis testing and testing a hypothesis are used interchangeably. We can, therefore, test a statement to determine whether the sample does or does not support the statement concerning the population. As noted in Chapter 8, an alternative to measuring or interviewing the entire population is to take a sample from the population. Likewise, the quality assurance department at Cooper Tire cannot check each tire produced to determine whether it will last more than 60,000 miles. For example, it would not be possible to contact every systems analyst in the United States to find his or her monthly income. 43.) In most cases the population is so large that it is not feasible to study all the items, objects, or persons in the population. (Source: American Academy of Ophthalmology Journal, San Francisco, Vol. In 5 percent of future cases, this expectation will not be met. When a person decides to have the surgery, he or she expects to reject the null hypothesis. The 5 percent represents a Type I error rate. The sample data of LASIK surgery shows that 5 percent of all cases result in complications. In a statistical sense, the research tests a null hypothesis that the surgery will not improve eyesight with the alternative hypothesis that the surgery will improve eyesight. Research shows that about 5 percent of all surgeries involve complications such as glare, corneal haze, over-correction or under-correction of vision, and loss of vision. HYPOTHESIS A statement about a population parameter subject to verification.ģ 332 Chapter 10 Statistics in Action LASIK is a 15-minute surgical procedure that uses a laser to reshape an eye s cornea with the goal of improving eyesight. We define a statistical hypothesis as follows. In statistical analysis we make a claim, that is, state a hypothesis, collect data, then use the data to test the assertion. On the basis of the symptoms, the physician will order certain diagnostic tests, then, according to the symptoms and the test results, determine the treatment to be followed.
In a similar sense, a patient goes to a physician and reports various symptoms.
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A jury hypothesizes that a person charged with a crime is innocent and subjects this hypothesis to verification by reviewing the evidence and hearing testimony before reaching a verdict. In the United States legal system, a person is innocent until proven guilty. To begin we need to define the word hypothesis. Data are then used to check the reasonableness of the statement. What Is a? A hypothesis is a statement about a population. A hypothesis is a statement about a population parameter. In the last section of the chapter, we describe possible errors due to sampling in hypothesis testing. Then we conduct tests of hypothesis for means and proportions. Next, we outline the steps in statistical hypothesis testing. We begin by defining what we mean by a statistical hypothesis and statistical hypothesis testing. This chapter and several of the following chapters are concerned with statistical hypothesis testing.
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Eighty percent of those who regularly play the state lotteries never win more than $100 in any one play. Thirty-five percent of retirees in the upper Midwest sell their home and move to a warm climate within 1 year of their retirement. The 2005 mean starting salary in sales for a graduate of a four-year college is $37,130. The mean time an American family lives in a particular single-family dwelling is 11.8 years. The mean number of miles driven by those leasing a Chevy TrailBlazer for three years is 32,000 miles. Some examples of statements we might want to test are: The mean speed of automobiles passing milepost 150 on the West Virginia Turnpike is 68 miles per hour. In this chapter, rather than develop a range of values within which we expect the population parameter to occur, we develop a procedure to test the validity of a statement about a population parameter. A confidence interval is a range of values within which we expect the population parameter to occur. Chapter 9 continued the study of statistical inference by developing a confidence interval. In other words, we estimated a population parameter from a sample statistic. For example, we selected a sample of 5 employees at Spence Sprockets, found the number of years of service for each sampled employee, computed the mean years of service, and used the sample mean to estimate the mean years of service for all employees. We described how we could select a random sample and from this sample estimate the value of a population parameter. 2 One-Sample Tests of 331 Introduction Chapter 8 began our study of statistical inference.
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