Question

In: Statistics and Probability

For each statement below circle TRUE if the statement is true, otherwise circle FALSE.

For each statement below circle TRUE if the statement is true, otherwise circle FALSE.

A hypothesis test uses data from a sample to assess a claim about a population.

A randomization distribution will be centered at the value used in the null hypothesis.

“Failing to reject the null hypothesis” and “accepting the null hypothesis” mean the same thing in a hypothesis test’s conclusion.

The p-value is the probability, assuming the alternative hypothesis is true, of obtaining a sample statistic as extreme as (or more extreme than) the observed sample statistic.

A p-value of 0.003 gives stronger evidence for the alternative hypothesis than a p-value of 0.450.

Solutions

Expert Solution

1 . A hypothesis test uses data from a sample to assess a claim about a population.- TRUE

Using Hypothesis Testing, we try to interpret or draw conclusions about the population using sample data.

2. A randomization distribution will be centered at the value used in the null hypothesis. - TRUE

Randomization distributions are always centered around the null hypothesized value. A randomization distribution is centered at the value of the parameter given in the null hypothesis.

3. “Failing to reject the null hypothesis” and “accepting the null hypothesis” mean the same thing in a hypothesis test’s conclusion. - TRUE

“Failing to reject the null hypothesis” is an odd way to state that the results of your hypothesis test are not statistically significant or i.e when we reject the alternative hypothesis.

While “accepting the null hypothesis” sounds more straightforward, although it is not statistically correct to say , but here also we accept null hypothesis which implies we reject the alternative hypothesis.

Hence “Failing to reject the null hypothesis” and “accepting the null hypothesis” may both sounds different but mean the same thing in a hypothesis test’s conclusion i.e we rejected the alternative hypothesis .

4. The p-value is the probability, assuming the alternative hypothesis is true, of obtaining a sample statistic as extreme as (or more extreme than) the observed sample statistic. _ FALSE

In statistics, the p-value is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. Hence these option is FALSE

5. A p-value of 0.003 gives stronger evidence for the alternative hypothesis than a p-value of 0.450 - TRUE

A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

Hence p-value of 0.003 gives stronger evidence for the alternative hypothesis and p-value of 0.450 gives stronger evidence against the alternative hypothesis ( i.e some evidence for the null hypothesis )


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