Question

A null and alternative hypothesis are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tailed. ​: ​: What type of test is being conducted in this​ problem?

Answer 1

Complete question is;

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

H0: μ = 4

H1: μ > 4

What type of test is being conducted in this problem? What parameter is being tested?

Answer:

Type of test = right tailed

Parameter being tested = population mean

Step-by-step explanation:

We are given the null and alternative hypothesis as;

H0: μ = 4

H1: μ > 4

Now, let's define terms;

The right tailed test and the left tailed test are both examples of one-tailed tests. This is because the area where we would reject the null hypothesis is only in one tail. Which means that in the case of left tail, the rejection region will occur only to the left of the graph while for the right tail, the rejection region will occur only to the right of the graph.

Whereas, for two tailed test, the area where we would reject the null hypothesis would not just be in one tail or one side of the graph but could be in either tail or either side of the graph. Hence, the name "two - tail".

Now, applying this to the question, the alternative hypothesis says the mean is greater than 4. On, a graph, an increase in number on the x-axis means going to the right. Thus, it is a right tailed test

Now, the sample being tested is population mean because in statistics, the symbol μ is generally used to denote population mean.