Examine the given statement, then express the null hypothesis and alternative hypothesis in symbolic form. Do not try to test it.

Question

The proportion of people aged 18 to 25 who currently use illicit drugs is equal to 0.3

a) p=0.3

b) p
0.3

c) p>0.3

d)p<0.3

e) p
0.3

f) p
0.3

The null hypothesis is
[ Select ]
.

The alternative hypothesis is

Answer 1

To express the null hypothesis and alternative hypothesis in symbolic form for the given statement, we start by defining \( p \) as the proportion of people aged 18 to 25 who currently use illicit drugs.

The statement to be tested is that the proportion is equal to 0.3.

1. The null hypothesis (\( H_0 \)) states that the proportion is equal to 0.3:

   • \( H_0: p = 0.3 \)

2. The alternative hypothesis (\( H_a \)) states that the proportion is not equal to 0.3:

   • \( H_a: p \neq 0.3 \)

Based on the options provided:

• The null hypothesis is (a) \( p = 0.3 \).
• The alternative hypothesis is not explicitly stated in the provided options, but it would correspond to \( p \neq 0.3 \), which is not listed.

Thus, your selection would be:

The null hypothesis is (a) \( p = 0.3 \). The alternative hypothesis is (e) \( p \neq 0.3 \) (implied, no exact match in options).