Depends on whether the alternative is one sided or two sided, and if two-sided, whether it is symmetric.
One sided: p < 0.05
Two sided, symmetrical: p < 0.025
To reject null hypothesis, because there is a very low probability (below the significance level) that the observed values would have been observed if the hypothesis were true.
2.58
To start with you select your hypothesis and its opposite: the null and alternative hypotheses. You select a confidence level (alpha %), which is the probability that your testing procedure rejects the null hypothesis when, if fact, it is true.Next you select a test statistic and calculate its probability distribution under the two hypotheses. You then find the possible values of the test statistic which, if the null hypothesis were true, would only occur alpha % of the times. This is called the critical region.Carry out the trial and collect data. Calculate the value of the test statistic. If it lies in the critical region then you reject the null hypothesis and go with the alternative hypothesis. If the test statistic does not lie in the critical region then you have no evidence to reject the null hypothesis.
Statistical tests compare the observed (or more extreme) values against what would be expected if the null hypothesis were true. If the probability of the observation is high you would retain the null hypothesis, if the probability is low you reject the null hypothesis. The thresholds for high or low probability are usually set arbitrarily at 5%, 1% etc. Strictly speaking, when rejecting the null hypothesis, you do not accept the alternative hypothesis because it is possible that neither are true and it is the model itself that is wrong.
When we state that the data analysis suggests that we "Reject the null hypothesis" we are stating that the sample statistic is sufficiently different from our assumed value of the population that it is unlikely to be explained by chance. If we use for example, that under the null hypothesis that engineers make on the average $120,000 per year. If we consider that the test statistic (size n) is normally distributed, we can use a two-tail test with an level of significance "alpha" to identify the lower and upper rejection zones on the normal distributon. If the test statistic falls in the non-rejection zone, we state that the "null hypothesis is not rejected." There are many good websites on hypothesis testing. Wikipedia provides a good summary of controversy on hypothesis testing. I note that some of the controversy stems from the idea that hypothesis testing will prove or validate population parameters, which is really beyond the scope of hypothesis testing theory. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing A second way to determine whether the null hypotheis is to calculate p-values. For this, please see: http://en.wikipedia.org/wiki/P-value
Any value greater than 0.05
To reject null hypothesis, because there is a very low probability (below the significance level) that the observed values would have been observed if the hypothesis were true.
The null hypothesis will not reject - it is a hypothesis and is not capable of rejecting anything. The critical region consists of the values of the test statistic where YOU will reject the null hypothesis in favour of the expressed alternative hypothesis.
you do not need to reject a null hypothesis. If you don not that means "we retain the null hypothesis." we retain the null hypothesis when the p-value is large but you have to compare the p-values with alpha levels of .01,.1, and .05 (most common alpha levels). If p-value is above alpha levels then we fail to reject the null hypothesis. retaining the null hypothesis means that we have evidence that something is going to occur (depending on the question)
2.58
I take this to be a significance of 0.04. To obtain the critical z-values I used wolfram.alpha.com with the following expression:P[-2.05
What is the significance of negative values of voltage and current?Negative values show direction and that is the significance
To start with you select your hypothesis and its opposite: the null and alternative hypotheses. You select a confidence level (alpha %), which is the probability that your testing procedure rejects the null hypothesis when, if fact, it is true.Next you select a test statistic and calculate its probability distribution under the two hypotheses. You then find the possible values of the test statistic which, if the null hypothesis were true, would only occur alpha % of the times. This is called the critical region.Carry out the trial and collect data. Calculate the value of the test statistic. If it lies in the critical region then you reject the null hypothesis and go with the alternative hypothesis. If the test statistic does not lie in the critical region then you have no evidence to reject the null hypothesis.
Statistical tests compare the observed (or more extreme) values against what would be expected if the null hypothesis were true. If the probability of the observation is high you would retain the null hypothesis, if the probability is low you reject the null hypothesis. The thresholds for high or low probability are usually set arbitrarily at 5%, 1% etc. Strictly speaking, when rejecting the null hypothesis, you do not accept the alternative hypothesis because it is possible that neither are true and it is the model itself that is wrong.
The rules are as follows:the hypothesis and its alternative are clearly spelled out before you look at he data,the observations are obtained randomly,the test statistic is based only on the observed data,you have measures of what the likely values of the test statistic if the [null] hypothesis were true and if it were not,you then reject the null hypothesis if the likelihood of obtaining a test statistic which is as or more extreme than observed is smaller than some predetermined (but arbitrary) value. Otherwise you accept the hypothesis.
Authors are individuals, they can accept or reject any ideas that they wish.
When we state that the data analysis suggests that we "Reject the null hypothesis" we are stating that the sample statistic is sufficiently different from our assumed value of the population that it is unlikely to be explained by chance. If we use for example, that under the null hypothesis that engineers make on the average $120,000 per year. If we consider that the test statistic (size n) is normally distributed, we can use a two-tail test with an level of significance "alpha" to identify the lower and upper rejection zones on the normal distributon. If the test statistic falls in the non-rejection zone, we state that the "null hypothesis is not rejected." There are many good websites on hypothesis testing. Wikipedia provides a good summary of controversy on hypothesis testing. I note that some of the controversy stems from the idea that hypothesis testing will prove or validate population parameters, which is really beyond the scope of hypothesis testing theory. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing A second way to determine whether the null hypotheis is to calculate p-values. For this, please see: http://en.wikipedia.org/wiki/P-value