Answer:
H0: u ≤ 10
Ha: u > 10
A right-tailed test
Step-by-step explanation:
In hypothesis testing there are two types of hypotheses;
The null hypothesis, H0 and the alternative hypothesis, Ha. The null hypothesis is the hypothesis of no difference and as such it always has an equality sign;
=, ≤, ≥
On the other hand the alternative hypothesis complements the null hypothesis meaning that if the null hypothesis is rejected then we take the alternative hypothesis to be true.
In order to identify the null and alternative hypothesis we look out for specific key words that will provide us with information on the type of inequality sign. In this scenario, the coach claims that the average number of fouls committed per game is no more than 10. Since µ represents the team's average number of fouls per game, this statement can be written in mathematical symbols as;
u ≤ 10, that is u is no more than 10; average number of fouls committed per game is no more than 10.
This statement will be our null hypothesis since it contains an equality sign.
H0: u ≤ 10
The complement of this statement will enable us deduce the alternative hypothesis. The complement of this statement can be found in the claim of the second coach who thinks that these players create more fouls, to be specific more than 10 fouls. In mathematical notation this claim can be written as;
u > 10, more than 10 fouls.
This statement will be our alternative hypothesis since it complements the null hypothesis;
Ha: u > 10
The type of significance test to be carried out in hypothesis testing emanates from the inequality sign of the alternative hypothesis. The following are the key points to note, if the alternative hypothesis contains;
≠, then this automatically becomes a two tailed test
<, then this automatically becomes a left tailed test since the inequality sign is pointing towards the left.
>, then this automatically becomes a right tailed test since the inequality sign is pointing towards the right.
Our alternative hypothesis contains >, hence this will be a right-tailed test
.
