Question

The primary concern is deciding whether the mean of Population 2 is less than the mean of Population$1.$

Short answer

(a) Null hypotheses:$H_0:{\mu }_1\le {\mu }_2$

Alternate hypotheses:$H_a:{\mu }_1>{\mu }_2$

(b) The hypotheses test has a right-tailed distribution.

Step-by-step solution

Part (a) Step 1: Given information  

Given in the question that, We need to determine the null and alternative hypotheses.

Part (a) Step 2: Explanation

A hypothesis is a testable hypothesis. The hypothesis is tested using a variety of statistical models.

A frequently accepted fact is referred to as a null hypothesis. The null hypotheses are rejected, disproved, or nullified by researchers. The researcher proposes an alternative hypothesis to refute the null hypothesis.

The major problem in the scenario is determining whether Population 2's mean is less than Population 1's mean.

First, it is assumed that Population 2's mean is greater than or equal to Population 1's mean. In other words, population 1's mean is smaller than or equal to population 2's mean. After that, the researcher seeks to disprove the null hypotheses.

Null hypotheses:$H_0:{\mu }_1\le {\mu }_2$

Alternate hypotheses:$H_a:{\mu }_1>{\mu }_2$

Part (b) Step 1: Given information  

Given in the question that, we need to classify the hypothesis test as two tailed, left tailed, or right tailed.

Part (b) Step 2: Explanation

The key focus in the provided scenario is determining if the mean of Population 2 is smaller than the mean of Population 1 To begin with, it is assumed that the mean of Population 2 is greater than or equal to the mean of Population 1. In other words, population 1's mean is smaller than or equal to population 2's mean. After that, the researcher seeks to disprove the null hypotheses.

Null hypotheses:$H_0:{\mu }_1\le {\mu }_2$

Alternate hypotheses: $H_a:{\mu }_1>{\mu }_2$

Alternate hypotheses can be tested from the right side of the normal distribution curve. As a result, the hypotheses test has a right-tailed distribution.