Q: When p value is less than the t value do I need to reject the null?

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In order to solve this you need the null hypothesis value also level of significance only helps you decide whether or not to reject the null hypothesis, is the p-value is above this then you do not reject the null hypothesis, if it is below you reject the null hypothesis Level of significance has nothing to do with the math

Probability of failing to reject a false null hypothesis.

In hypothesis testing, this is the probability of failing to reject a false null hypothesis.

It is conventionally 5% (or lower) but there is no good reason for that level.

You should reject the null hypothesis.

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In order to solve this you need the null hypothesis value also level of significance only helps you decide whether or not to reject the null hypothesis, is the p-value is above this then you do not reject the null hypothesis, if it is below you reject the null hypothesis Level of significance has nothing to do with the math

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)

A p-value is the probability of obtaining a test statistic as extreme or more extreme than the one actually obtained if the null hypothesis were true. If this p-value is less than the level of significance (usually set by the experimenter as .05 or .01), we reject the null hypothesis. Otherwise, we retain the null hypothesis. Therefore, a p-value of 0.66 tell us not to reject the null hypothesis.

We have two types of hypothesis i.e., Null Hypothesis and Alternative Hypothesis. we take null hypothesis as the same statement given in the problem. Alternative hypothesis is the statement that is complementary to null hypothesis. When our calculated value is less than the tabulated value, we accept null hypothesis otherwise we reject null hypothesis.

At a probability of 0.5 you cannot reject the null hypothesis!

When probability value (p-value) is greater than alpha value, we fail to reject the null hypothesis.Probablity value is the probability of obtaining an answer equal to or more extreme than the observed value.Alpha value is the level of significance. It's the value set that determines if a result is statistically significant, or in other words, if it's not likely to have occurred simply due to chance. Alpha value is usually 5%.There are two hypotheses when we conduct a hypothesis test: the null hypothesis and the alternative hypothesis.The null hypothesis acts as a default position. It's usually an assumption that there is no relationship between two events or that a treatment has no effect. In most legal systems, the null hypothesis would be that the defendant is innocent.The alternative hypothesis is what we would assume if we reject the null hypothesis. We reject the null hypothesis when the probability value is less than the alpha value.

Probability of failing to reject a false null hypothesis.

The z-score is a statistical test of significance to help you determine if you should accept or reject the null-hypothesis; whereas the p-value gives you the probability that you were wrong to reject the null-hypothesis. (The null-hypothesis proposes that NO statistical significance exists in a set of observations).

In hypothesis testing, this is the probability of failing to reject a false null hypothesis.

NO!

You chose whether or ot to reject the null hypothesis. Or you repeat the experiment.

It is conventionally 5% (or lower) but there is no good reason for that level.