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A hypothesis (from Greeká½‘Ï€ÏŒÎ¸ÎµÏƒÎ¹Ï‚; plural hypotheses) is a proposed explanation for an observable phenomenon. The term derives from the Greek, á½‘Ï€Î¿Ï„Î¹Î¸ÎÎ½Î±Î¹ â€“ hypotithenai meaning "to put under" or "to suppose." For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously in common and informal usage, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis.
In a related but distinguishable usage, the term hypothesis is used for the antecedent of a proposition; thus in proposition "If P, then Q", P denotes the hypothesis (or antecedent); Q can be called a consequent. P is the assumption in a (possibly counterfactual) What Ifquestion.
The adjective hypothetical, meaning "having the nature of a hypothesis," or "being assumed to exist as an immediate consequence of a hypothesis," can refer to any of these meanings of the term "hypothesis."
In Plato's Meno(86eâ€“87b),Socrates dissects virtue with a method used by mathematicians, that of "investigating from a hypothesis." In this sense, 'hypothesis' refers to a clever idea or to a convenient mathematical approach that simplifies cumbersome calculations. Cardinal Bellarmine gave a famous example of this usage in the warning issued to Galileo in the early 17th century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.
In common usage in the 21st century, a hypothesis refers to a provisional idea whose merit requires evaluation. For proper evaluation, the framer of a hypothesis needs to define specifics in operational terms. A hypothesis requires more work by the researcher in order to either confirm or disprove it. In due course, a confirmed hypothesis may become part of a theory or occasionally may grow to become a theory itself. Normally, scientific hypotheses have the form of a mathematical model. Sometimes, but not always, one can also formulate them as existential statements, stating that some particular instance of the phenomenon under examination has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.
Any useful hypothesis will enable predictions by reasoning (including deductive reasoning). It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction may also invoke statistics and only talk about probabilities. Karl Popper, following others, has argued that a hypothesis must be falsifiable, and that one cannot regard a proposition or theory as scientific if it does not admit the possibility of being shown false. Other philosophers of science have rejected the criterion of falsifiability or supplemented it with other criteria, such as verifiability (e.g., verificationism) or coherence (e.g., confirmation holism). The scientific method involves experimentation on the basis of hypotheses to answer questions and explore observations.
In framing a hypothesis, the investigator must not currently know the outcome of a test or that it remains reasonably under continuing investigation. Only in such cases does the experiment, test or study potentially increase the probability of showing the truth of a hypothesis. If the researcher already knows the outcome, it counts as a "consequence" â€” and the researcher should have already considered this while formulating the hypothesis. If one cannot assess the predictions by observation or by experience, the hypothesis classes as not yet useful, and must wait for others who might come afterward to make possible the needed observations. For example, a new technology or theory might make the necessary experiments feasible.
People refer to a trial solution to a problem as a hypothesis â€” often called an "educated guess" â€” because it provides a suggested solution based on the evidence. Experimenters may test and reject several hypotheses before solving the problem.
According to Schick and Vaughn, researchers weighing up alternative hypotheses may take into consideration:
- Testability (compare falsifiability as discussed above)
- Simplicity (as in the application of "From Yahoo Answers
Question:For this problem, my tutor said the null and alternative hpothesis is: Ho: u=3 H1: u is not equal to three Is that right. I am not trying to be disrespectful to him, it's just my book has a different answer, but my book could be wrond. Problem: A manufacturer of electronic kits has found that the mean time needed for novices to assemble its new circuit tester is 3 hours, with a standard deviation of .20 hours. A consltant has made a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 15 novices require a mean of 2.9 hours to complete the job. Assuming the population of times is normally distributed, and using the .05 level of significance, should we conclude the new booklet is effective?
Answers:This is the final version of my answer. Yes, you are right at the extent that the null hypothesis is the manufacturer's claim of mean, U equal to 3 hours that the consultant want to reject. However, the alternative hypothesis that the consultant in favor of is is the mean, U should be less than 3(that is one sided-test), based on because the mean of the random particular sample that he obtained is 2.9, which is less than 3. We wish to test Ho: U = 3. in favor of Ha: U< 3. We are given that the population of times is normally distributed, x-bar =2.9, s = = 0.20 and n=15. According to the central limit theorem, since this particular sample with size of n= 15 is less than 30, so we should use the t distribution to describe the sampling distribution of x-bar which is very similiar or approximately to the standard normal curve but is more spread out. Degrees of freedom for this hypothesis testing = n-1 = 15-1 = 14 The test static = t = (x-bar - U)/ ( / n) = (x-bar - U)/ (s/ n) = (2.9-3)/ (0.20/ 15) = -1.9365 We can only reject Ho in favor of Ha if and only if t<-t which -t is based on (n-1) degrees of freedom. Given we have to use = 0.05 level of significance, the rejection point = -t ;(n-1)d.f.= -t0.05;(15-1)d.f. = -t0.05;14d.f. =-1.761 The p-value for this hypothesis testing = the rejection area on the left end or tail of the critical value t under the t distribution curve= -1.9365;(n-1) =(15-1) = 14 degrees of freedom= -0.025 Since t= -1.9365 is less than that of -t ;14d.f. = -1.761, then we can reject Ho in favor of Ha, based on this particular random sample that the consultant selected. Since the p-value that we calculated here is -0.025 which is reasonably less than -t ;14d.f. = -0.05, so we have sufficient evidence to conclude that the new booklet is effective.Question:The EPA wants to show that the mean carbon monoxide level of airpollution is higher than 4.9. Does a random sample of 22 readings (mean = 5.1, s = 1.17 ) present sufficient evidence to support the EPA's claim? use alpha = .05 (such readings are normal distributions) a. State the null and alternate hypotheses. b. Calculate the t test statistic c. find the critical values and critical regions d. state the conclusion e. approximate the p-value for this test
Answers:Preliminary: We assume that the variable X=(CO-level) has a Normal Distribution N[4.9,si], with unknown standard dev. si. a) null hypothesis: The random sample S(22,5.1,1.17) is from a M(4.9,si) distribution altenative: S is from a ND with mu>4.9 (because the claim is:"higher") b) The test statistic for a Student-t test is t=sqrt(n)(x-bar-mu)/s= sqrt(22)(5.1-4.9)/1.17=1.098. c) We have to find c from P(TQuestion:I need help solving this problem, please show the steps and how you got the answer. The top food snacks consumed by adults aged 18 54 are gum, chocolate candy, fresh fruit, potato chips, breath mints/candy, ice cream, nuts, cookies, bars, yogurt, and crackers. Out of a random sample of 25 men, 15 ranked fresh fruit in their top five snack choices. Out of a random sample of 32 women, 22 ranked fresh fruit in their top five snack choices. Is there a difference in the proportion of men and women who rank fresh fruit in their top five list of snacks? (a) State the hypotheses and a decision rule for = .10. (b) Calculate the sample proportions. (c) Find the test statistic and its p-value. What is your conclusion? (d) Is normality assured? (Data are from The NPD Group press release, Fruit #1 Snack Food Consumed by Kids, June 16, 2005.)
Answers:Salaam, This belongs in chemistry Peace ^_^Question:Can anyone assist me with conducting a hypothesis test on this problem? Scores for a standardized reading test are normally distributed with mu=50 and s=6 for 6th graders. A teacher suspects his class is way above the average. His class is given a standardized test and the mean is 54.5 and the number of students=16. Conduct a hypothesis test with a=.05.
Answers:To do this, you need to have a table of the critical values for a t distribution (you're doing a t-test to compare a mean of a sample - the class - to the mean of the "population" - the previous students who have taken the test). Here's one if you don't have one handy: http://www.theseashore.org.uk/theseashore/Stats%20for%20twits/critical%20values%20of%20t.jpg To find your t value, you must first use the other information you're given to calculate the standard deviation of the mean of the sample. To do this, you fist need to calculate the variance, which is s^2 (s squared) = 36 (=6 x 6). To get the standard deviation of the mean of the sample, divide the variance by your sample size, then take the square root of your result: 36/16 = 2.25, and the squre root of 2.25 = 1.5 Now, to calculate the t score for your sample, first subtract the mean score of the population from the mean score of your class and divide your result by the standard deviation of the mean of the sample: (54.5-50)/1.5 = 3 So your t value is 3. Your degrees of freedom is 15 (one less than your sample size). Next, you compare your value with the table for the t distribution. If you have a table with two values at the top (alpha, or a 1 and alpha or a 2), you want to use the a1. The difference here is if you're predicting a "direction" for your result, such as "will be more than, or will be less than, it's a one-tailed test and you want to use the a1. If you're just saying there will be a difference, without saying higher or lower, it's a two-tailed test and you would use a2. Since the teacher in your problem thinks his students are above average, you'll be looking for a score above the population mean, so this is a one-tailed test. Go down the rows for the degrees of freedom at the left side of the table to 15, then across to the 5% (0.05) significance level and you'll see the critical t value is 1.753. Because your sample value of t (3) is greater than the critical value of 1.753. you conclude that the teacher is correct in that his class scored siginificantly higher than average on the standardized test. NOTE: This isn't a Botany question, but a Mathematics/stastistics question. Please be sure you post your question to the correct category for the best answers - you can change the category from the automatic selection (which is often wrong in its selection) before you submit it.
From YoutubeHypothesis Testing on the TI-83 and TI-84 Calculator :This video shows how to conduct a hypothesis test on the TI-83/84 calculator. For much more detailed information on hypothesis testing and all other calculator functions, click here: shop.ebay.comStatistics - 6 - Hypothesis Testing - 8 - Calculating the Test Statistic :This discussion examines the methodology for determining a test statistic using the infamous E/SE.