STATS Test 3

What is a hypothesis in​ statistics?

A hypothesis is a claim about a population parameter​ (such as a population​ proportion, p, or a population​ mean, muμ​) or some other characteristic of a population.

What is meant by a hypothesis test in​ statistics? Choose the correct answer below.

A hypothesis test is a standard procedure for testing a claim about the value of a population parameter.

What is a type I​ error? What is a type II​ error?

A type I error is the mistake of rejecting the null hypothesis when the null hypothesis is actually true. A type II error is the mistake of failing to reject the null hypothesis when the null hypothesis is actually false.

How does this compare to the critical values for statistical significance for a population​ mean?

The critical values are the same as those used with population means.

What do we mean by critical values for significance in a hypothesis test for the population​ proportion?

The critical values are the standard scores required for statistical significance at a given level.

How do we use this for making decisions about the hypothesis​ test?

The level of statistical significance is determined by comparing the standard score to the critical values.

In interpreting a​ P-value of 0.42​, a researcher states that the results are statistically significant because the​ P-value is less than​ 0.5, indicating that the results are not likely to occur by chance.

The statement does not make sense. A​ P-value of .42 corresponds to results that are likely to occur by chance.

Because the significance level is the probability of making a type I​ error, it is wise to select a significance level of zero so that there is no probability of making that error.

The statement does not make sense. It is impossible to have no probability of a type I error.

In hypothesis​ tests, if the significance level is​ 0.01, then the​ P-value is also 0.01.

The statement does not make sense. The significance level and the​ P-value represent different components of the hypothesis​ test, and are generally not the same.

In testing a claim about a population​ mean, if the standard score for a sample mean is z=​0, then there is not sufficient sample evidence to support the alternative hypothesis.

The statement makes sense. A standard score of 0 represents the peak of the sampling​ distribution, so it is a likely outcome if the null hypothesis is true.

What do​ p, p hat​, and​ P-value represent?

The symbol p represents the proportion in a​ population, ModifyingAbove p with caretp represents the proportion in a​ sample, and the​ P-value is the probability of getting a sample proportion that is at least as extreme as the sample proportion actually observed given that the null hypothesis is true.

The results of my hypothesis test were statistically significant at the 0.01​ level, so no one can doubt my claim any longer.

This statement does not make sense. Statistical significance at the 0.01 level still implies a​ 1% chance that the result is in​ error, leaving room for reasonable doubt.

To learn about smartphone​ ownership, I chose a null hypothesis claiming that the proportion of adults who own a smartphone is equal to​ 0.8, and the result of my hypothesis test proved this claim to be true.

This statement does not make sense. The null hypothesis is​ good, but the hypothesis test cannot result in accepting​ (or proving) the null hypothesis.