The null hypothesis, [tex]\rm H_{0}[/tex] for the given situation in the question, will be
[tex]\rm H_{0}:\mu\leq 10[/tex]
For finding the null hypotheses we will follow the data given in the question
The null hypothesis, [tex]\rm H_{0}[/tex] is the hypothesis of no difference and as such, it always has an equality sign;
=, ≤, ≥
In order to identify the null we lookout for specific keywords that will provide us with information on the type of inequality sign.
In this situation, 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;
[tex]\mu\leq 10[/tex]
That is [tex]\mu[/tex] is less than 10 and the average number of fouls committed per game is less than 10.
This statement will be our null hypothesis since it contains an equality sign.
[tex]\rm H_{0}:\mu\leq 10[/tex]
Thus null hypothesis, [tex]\rm H_{0}[/tex] for the given situation in the question, will be
[tex]\rm H_{0}:\mu\leq 10[/tex]
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