It is believed that the mean height of high school students who play basketball on the school team is $73$inches with a standard deviation of $1.8$inches. A random sample of $40$players is chosen. The sample mean was $71$inches, and the sample standard deviation was $1.5$years. Do the data support the claim that the mean height is less than $73$ inches? The p-value is almost zero. State the null and alternative hypotheses and interpret the p-value.

A basketball team's average height is $73$ inches, with a standard variation of $1.8$ inches. The football team's average height is $71$ inches, with a standard variation of $1.5$ inches.

The null hypothesis states that no statistical relationship exists between two variables, hence the researcher must always reject the inference.

The alternative hypothesis suggests that the two variables have a significant relationship.

For the provided data, the null and alternate hypotheses are:

$$\begin{gathered} H_0:\mu \ge 73 \\ {H}_a:\mu <73 \end{gathered}$$

Because the p-value is set to zero, the alpha level is set to$5\%.$ The null hypothesis is rejected at this alpha level because the p-value is less than $0.05$. As a result, there is sufficient evidence to support the assertion that the average height of the basketball team's players is less than $73$ inches.