Question

Hypothesis testing conceptual questions: a. Define the null and alternative hypothesis b. What are the two errors that can occur in hypothesis testing? What mathematical symbols are used to denote these errors? c. Define the P-value. How are P-values used in hypothesis testing? d. How is the significance level of a hypothesis test determined? e. What assumptions must your data meet in order to perform a hypothesis test?

Answer 1

Here,

The hypothesis is the tentative statement about population.

a) Null Hypothesis : null hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. According to professor R.A Fisher null hypothesis is the hypothesis that tested for its possible rejections.

Alternative Hypothesis :

An alternative hypothesis simply is the inverse, or opposite, of the null hypothesis. The alternative Hypothesis is also called as Research Hypothesis.

B) Two type of Error :

In hypothesis there are two Types of error.

First one is Type l error and Type ll error.

Type l error : the making the decision that Rejecting Ho when Ho is true.

Type ll error : Tge making of decision that Rejecting H1 when H1 is true.

The Probability of commenting type l error is denoted by Alph. Similarly the probability of commenting type ll error is denoted by Beta.

c) P- Value :

The p value is the probability value of test Statistic.

The p value is used in hypothesis test to help you accept or reject the Ho hypothesis. The p value is the evidence against a Ho hypothesis. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Alpha levels are controlled by the researcher and are related to confidence levels. You get an alpha level by subtracting your confidence level from 100%.

A small p (≤ 0.05), reject the null hypothesis. This is strong evidence that the null hypothesis is invalid.

A large p (> 0.05) means the alternate hypothesis is weak, so you do not reject the null.

d) The significance level is denoted by Alpha and it is the probability of making Type I error.

Suppose a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

The significance level determines how far out from the null hypothesis value we'll draw that line on the graph. To graph a significance level of 0.05, we need to shade the 5% of the distribution that is furthest away from the null hypothesis.

e) Assumptions while performing Hypothesis test :

Different hypothesis tests make different assumptions about the distribution of the random variable being sampled in the data. These assumptions must be considered when choosing a test and when interpreting the results.

For example, the z-test and the t-test both assume that the data are independently sampled from a normal distribution.

Both the z-test and the t-test are relatively robust with respect to departures from this assumption, so long as the sample size n is large enough. Both tests compute a sample mean Xbar which, by the Central Limit Theorem, has an approximately normal sampling distribution with mean equal to the population mean μ, regardless of the population distribution being sampled.

These are the major assumptions made during hypothesis test.

Hope you understood about Hypothesis test. If you understood then RATE POSITIVE ?.in case of any queries please feel free to ask in comment box.

Thank you.