Question

for the following conjecture, state the null and alternative hypotheses.

the average age of first-year medical school students is less than 27 years.

the null hypothesis is \\(h_0\\) :

the alternative hypothesis is \\(h_1\\) :

Explanation:

Identify the parameter of interest

The conjecture mentions "The average age of first-year medical school students".
We represent the population mean age with the parameter \(\mu\).

Formulate the alternative hypothesis

The conjecture states that the average age is "less than 27 years".
This claim represents a strict inequality, which forms the alternative hypothesis:

$$H_1: \mu < 27$$

Formulate the null hypothesis

The null hypothesis is the statement of no effect or status quo, which is the complement of the alternative hypothesis.
It contains the equality condition:

$$H_0: \mu \ge 27$$

(Note: In many introductory statistics courses, the null hypothesis is written with a strict equality as \(H_0: \mu = 27\). We will provide both standard representations).

Answer:

For the following conjecture, state the null and alternative hypotheses.

The average age of first-year medical school students is less than 27 years.

The null hypothesis is \(H_0:\) <blank>\(\mu \ge 27\)</blank> (or <blank>\(\mu = 27\)</blank>).

The alternative hypothesis is \(H_1:\) <blank>\(\mu < 27\)</blank>.